The Poset Of K Shapes And Branching Rules For K Schur Functions

Author : Thomas Lam,Luc Lapointe,Jennifer Morse,Mark Shimozono
Publisher : American Mathematical Soc.
Page : 101 pages
File Size : 40,9 Mb
Release : 2013-04-22
Category : Mathematics
ISBN : 9780821872949

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The Poset of $k$-Shapes and Branching Rules for $k$-Schur Functions by Thomas Lam,Luc Lapointe,Jennifer Morse,Mark Shimozono Pdf

The authors give a combinatorial expansion of a Schubert homology class in the affine Grassmannian $\mathrm{Gr}_{\mathrm{SL}_k}$ into Schubert homology classes in $\mathrm{Gr}_{\mathrm{SL}_{k+1}}$. This is achieved by studying the combinatorics of a new class of partitions called $k$-shapes, which interpolates between $k$-cores and $k+1$-cores. The authors define a symmetric function for each $k$-shape, and show that they expand positively in terms of dual $k$-Schur functions. They obtain an explicit combinatorial description of the expansion of an ungraded $k$-Schur function into $k+1$-Schur functions. As a corollary, they give a formula for the Schur expansion of an ungraded $k$-Schur function.

Author : Thomas Lam,Luc Lapointe,Jennifer Morse,Mark Shimozono
Publisher : Unknown
Page : 101 pages
File Size : 54,6 Mb
Release : 2013
Category : Partially ordered sets
ISBN : 0821898744

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The Poset of [kappa]-shapes and Branching Rules for [kappa]-Schur Functions by Thomas Lam,Luc Lapointe,Jennifer Morse,Mark Shimozono Pdf

We give a combinatorial expansion of a Schubert homology class in the affine Grassmannian GrSLk into Schubert homology classes in GrSLk+1. This is achieved by studying the combinatorics of a new class of partitions called k-shapes, which interpolates between k k-cores and kk+1-cores. We define a symmetric function for each k-shape, and show that they expand positively in terms of dual k-Schur functions. We obtain an explicit combinatorial description of the expansion of an ungraded k k-Schur function into k+1-Schur functions. As a corollary, we give a formula for the Schur expansion of an ungraded k-Schur function.

Author : Thomas Lam,Luc Lapointe,Jennifer Morse,Anne Schilling,Mark Shimozono,Mike Zabrocki
Publisher : Springer
Page : 226 pages
File Size : 52,9 Mb
Release : 2014-06-05
Category : Mathematics
ISBN : 9781493906826

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k-Schur Functions and Affine Schubert Calculus by Thomas Lam,Luc Lapointe,Jennifer Morse,Anne Schilling,Mark Shimozono,Mike Zabrocki Pdf

This book gives an introduction to the very active field of combinatorics of affine Schubert calculus, explains the current state of the art, and states the current open problems. Affine Schubert calculus lies at the crossroads of combinatorics, geometry, and representation theory. Its modern development is motivated by two seemingly unrelated directions. One is the introduction of k-Schur functions in the study of Macdonald polynomial positivity, a mostly combinatorial branch of symmetric function theory. The other direction is the study of the Schubert bases of the (co)homology of the affine Grassmannian, an algebro-topological formulation of a problem in enumerative geometry. This is the first introductory text on this subject. It contains many examples in Sage, a free open source general purpose mathematical software system, to entice the reader to investigate the open problems. This book is written for advanced undergraduate and graduate students, as well as researchers, who want to become familiar with this fascinating new field.

Author : Masaaki Furusawa,Kimball Martin, Joseph A. Shalika
Publisher : American Mathematical Soc.
Page : 134 pages
File Size : 49,6 Mb
Release : 2013-08-23
Category : Mathematics
ISBN : 9780821887424

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On Central Critical Values of the Degree Four L-Functions for GSp (4): The Fundamental Lemma. III by Masaaki Furusawa,Kimball Martin, Joseph A. Shalika Pdf

Some time ago, the first and third authors proposed two relative trace formulas to prove generalizations of Böcherer's conjecture on the central critical values of the degree four -functions for , and proved the relevant fundamental lemmas. Recently, the first and second authors proposed an alternative third relative trace formula to approach the same problem and proved the relevant fundamental lemma. In this paper the authors extend the latter fundamental lemma and the first of the former fundamental lemmas to the full Hecke algebra. The fundamental lemma is an equality of two local relative orbital integrals. In order to show that they are equal, the authors compute them explicitly for certain bases of the Hecke algebra and deduce the matching.

Author : Jean-Bernard Bru,Walter de Siqueira Pedra
Publisher : American Mathematical Soc.
Page : 155 pages
File Size : 47,5 Mb
Release : 2013-06-28
Category : Mathematics
ISBN : 9780821889763

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Non-cooperative Equilibria of Fermi Systems with Long Range Interactions by Jean-Bernard Bru,Walter de Siqueira Pedra Pdf

The authors define a Banach space $\mathcal{M}_{1}$ of models for fermions or quantum spins in the lattice with long range interactions and make explicit the structure of (generalized) equilibrium states for any $\mathfrak{m}\in \mathcal{M}_{1}$. In particular, the authors give a first answer to an old open problem in mathematical physics--first addressed by Ginibre in 1968 within a different context--about the validity of the so-called Bogoliubov approximation on the level of states. Depending on the model $\mathfrak{m}\in \mathcal{M}_{1}$, the authors' method provides a systematic way to study all its correlation functions at equilibrium and can thus be used to analyze the physics of long range interactions. Furthermore, the authors show that the thermodynamics of long range models $\mathfrak{m}\in \mathcal{M}_{1}$ is governed by the non-cooperative equilibria of a zero-sum game, called here thermodynamic game.

Author : Bruno Bianchini,Luciano Mari,Marco Rigoli
Publisher : American Mathematical Soc.
Page : 195 pages
File Size : 47,7 Mb
Release : 2013-08-23
Category : Mathematics
ISBN : 9780821887998

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On Some Aspects of Oscillation Theory and Geometry by Bruno Bianchini,Luciano Mari,Marco Rigoli Pdf

The aim of this paper is to analyze some of the relationships between oscillation theory for linear ordinary differential equations on the real line (shortly, ODE) and the geometry of complete Riemannian manifolds. With this motivation the authors prove some new results in both directions, ranging from oscillation and nonoscillation conditions for ODE's that improve on classical criteria, to estimates in the spectral theory of some geometric differential operator on Riemannian manifolds with related topological and geometric applications. To keep their investigation basically self-contained, the authors also collect some, more or less known, material which often appears in the literature in various forms and for which they give, in some instances, new proofs according to their specific point of view.

Author : Robert J. Buckingham,Peter D. Miller
Publisher : American Mathematical Soc.
Page : 136 pages
File Size : 49,7 Mb
Release : 2013-08-23
Category : Mathematics
ISBN : 9780821885451

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The Sine-Gordon Equation in the Semiclassical Limit: Dynamics of Fluxon Condensates by Robert J. Buckingham,Peter D. Miller Pdf

The authors study the Cauchy problem for the sine-Gordon equation in the semiclassical limit with pure-impulse initial data of sufficient strength to generate both high-frequency rotational motion near the peak of the impulse profile and also high-frequency librational motion in the tails. They show that for small times independent of the semiclassical scaling parameter, both types of motion are accurately described by explicit formulae involving elliptic functions. These formulae demonstrate consistency with predictions of Whitham's formal modulation theory in both the hyperbolic (modulationally stable) and elliptic (modulationally unstable) cases.

Author : Josef Bemelmans,Giovanni Paolo Galdi,Mads Kyed
Publisher : American Mathematical Soc.
Page : 89 pages
File Size : 48,5 Mb
Release : 2013-10-23
Category : Mathematics
ISBN : 9780821887738

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On the Steady Motion of a Coupled System Solid-liquid by Josef Bemelmans,Giovanni Paolo Galdi,Mads Kyed Pdf

The authors study the unconstrained (free) motion of an elastic solid $\mathcal B$ in a Navier-Stokes liquid $\mathcal L$ occupying the whole space outside $\mathcal B$, under the assumption that a constant body force $\mathfrak b$ is acting on $\mathcal B$. More specifically, the authors are interested in the steady motion of the coupled system $\{\mathcal B,\mathcal L\}$, which means that there exists a frame with respect to which the relevant governing equations possess a time-independent solution. The authors prove the existence of such a frame, provided some smallness restrictions are imposed on the physical parameters, and the reference configuration of $\mathcal B$ satisfies suitable geometric properties.

Author : Jose Luis Flores,J. Herrera,M. Sánchez
Publisher : American Mathematical Soc.
Page : 76 pages
File Size : 53,9 Mb
Release : 2013-10-23
Category : Mathematics
ISBN : 9780821887752

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Gromov, Cauchy and Causal Boundaries for Riemannian, Finslerian and Lorentzian Manifolds by Jose Luis Flores,J. Herrera,M. Sánchez Pdf

Recently, the old notion of causal boundary for a spacetime $V$ has been redefined consistently. The computation of this boundary $\partial V$ on any standard conformally stationary spacetime $V=\mathbb{R}\times M$, suggests a natural compactification $M_B$ associated to any Riemannian metric on $M$ or, more generally, to any Finslerian one. The corresponding boundary $\partial_BM$ is constructed in terms of Busemann-type functions. Roughly, $\partial_BM$ represents the set of all the directions in $M$ including both, asymptotic and ``finite'' (or ``incomplete'') directions. This Busemann boundary $\partial_BM$ is related to two classical boundaries: the Cauchy boundary $\partial_{C}M$ and the Gromov boundary $\partial_GM$. The authors' aims are: (1) to study the subtleties of both, the Cauchy boundary for any generalized (possibly non-symmetric) distance and the Gromov compactification for any (possibly incomplete) Finsler manifold, (2) to introduce the new Busemann compactification $M_B$, relating it with the previous two completions, and (3) to give a full description of the causal boundary $\partial V$ of any standard conformally stationary spacetime.

Author : Andrew Knightly,C. Li
Publisher : American Mathematical Soc.
Page : 132 pages
File Size : 42,6 Mb
Release : 2013-06-28
Category : Mathematics
ISBN : 9780821887448

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Kuznetsov's Trace Formula and the Hecke Eigenvalues of Maass Forms by Andrew Knightly,C. Li Pdf

The authors give an adelic treatment of the Kuznetsov trace formula as a relative trace formula on $\operatorname{GL}(2)$ over $\mathbf{Q}$. The result is a variant which incorporates a Hecke eigenvalue in addition to two Fourier coefficients on the spectral side. The authors include a proof of a Weil bound for the generalized twisted Kloosterman sums which arise on the geometric side. As an application, they show that the Hecke eigenvalues of Maass forms at a fixed prime, when weighted as in the Kuznetsov formula, become equidistributed relative to the Sato-Tate measure in the limit as the level goes to infinity.

Author : H. Inci,Thomas Kappeler,P. Topalov
Publisher : American Mathematical Soc.
Page : 60 pages
File Size : 43,9 Mb
Release : 2013-10-23
Category : Mathematics
ISBN : 9780821887417

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On the Regularity of the Composition of Diffeomorphisms by H. Inci,Thomas Kappeler,P. Topalov Pdf

For $M$ a closed manifold or the Euclidean space $\mathbb{R}^n$, the authors present a detailed proof of regularity properties of the composition of $H^s$-regular diffeomorphisms of $M$ for $s >\frac{1}{2}\dim M+1$.

Author : Philippe Gille,Arturo Pianzola
Publisher : American Mathematical Soc.
Page : 112 pages
File Size : 47,6 Mb
Release : 2013-10-23
Category : Mathematics
ISBN : 9780821887745

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Torsors, Reductive Group Schemes and Extended Affine Lie Algebras by Philippe Gille,Arturo Pianzola Pdf

The authors give a detailed description of the torsors that correspond to multiloop algebras. These algebras are twisted forms of simple Lie algebras extended over Laurent polynomial rings. They play a crucial role in the construction of Extended Affine Lie Algebras (which are higher nullity analogues of the affine Kac-Moody Lie algebras). The torsor approach that the authors take draws heavily from the theory of reductive group schemes developed by M. Demazure and A. Grothendieck. It also allows the authors to find a bridge between multiloop algebras and the work of F. Bruhat and J. Tits on reductive groups over complete local fields.

Author : Kening Lu,Qiudong Wang,Lai-Sang Young
Publisher : American Mathematical Soc.
Page : 85 pages
File Size : 44,7 Mb
Release : 2013-06-28
Category : Mathematics
ISBN : 9780821884843

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Strange Attractors for Periodically Forced Parabolic Equations by Kening Lu,Qiudong Wang,Lai-Sang Young Pdf

The authors prove that in systems undergoing Hopf bifurcations, the effects of periodic forcing can be amplified by the shearing in the system to create sustained chaotic behavior. Specifically, strange attractors with SRB measures are shown to exist. The analysis is carried out for infinite dimensional systems, and the results are applicable to partial differential equations. Application of the general results to a concrete equation, namely the Brusselator, is given.

Author : Rebecca Waldecker
Publisher : American Mathematical Soc.
Page : 150 pages
File Size : 41,5 Mb
Release : 2013-10-23
Category : Mathematics
ISBN : 9780821888032

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Isolated Involutions in Finite Groups by Rebecca Waldecker Pdf

This text provides a new proof of Glauberman's Z*-Theorem under the additional hypothesis that the simple groups involved in the centraliser of an isolated involution are known simple groups.

Author : Christopher P. Bendel,Daniel K. Nakano, Brian J. Parshal,Cornelius Pillen
Publisher : American Mathematical Soc.
Page : 93 pages
File Size : 51,8 Mb
Release : 2014-04-07
Category : Mathematics
ISBN : 9780821891759

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Cohomology for Quantum Groups via the Geometry of the Nullcone by Christopher P. Bendel,Daniel K. Nakano, Brian J. Parshal,Cornelius Pillen Pdf