The Weyl Character Formula

2004 ◽  
pp. 162-174
Author(s):  
Daniel Bump
Keyword(s):  
Character Formula ◽  
Weyl Character Formula

scholarly journals The elliptic Weyl character formula

2014 ◽  
Vol 150 (7) ◽  
pp. 1196-1234 ◽  
Author(s):  
Nora Ganter
Keyword(s):  
Line Bundle ◽  
Lie Groups ◽  
Theoretical Framework ◽  
Flag Variety ◽  
Schubert Calculus ◽  
Character Formula ◽  
Elliptic Cohomology ◽  
Image Position ◽  
Weyl Character Formula

AbstractWe calculate equivariant elliptic cohomology of the partial flag variety$\def \xmlpi #1{}\def \mathsfbi #1{\boldsymbol {\mathsf {#1}}}\let \le =\leqslant \let \leq =\leqslant \let \ge =\geqslant \let \geq =\geqslant \def \Pr {\mathit {Pr}}\def \Fr {\mathit {Fr}}\def \Rey {\mathit {Re}}G/H$, where$H\subseteq G$are compact connected Lie groups of equal rank. We identify the${\rm RO}(G)$-graded coefficients${\mathcal{E}} ll_G^*$as powers of Looijenga’s line bundle and prove that transfer along the map$$\begin{equation*} \pi \,{:}\,G/H\longrightarrow {\rm pt} \end{equation*}$$is calculated by the Weyl–Kac character formula. Treating ordinary cohomology,$K$-theory and elliptic cohomology in parallel, this paper organizes the theoretical framework for the elliptic Schubert calculus of [N. Ganter and A. Ram,Elliptic Schubert calculus, in preparation].

On the Weyl character formula forSU(n)

1976 ◽  
Vol 15 (3) ◽  
pp. 201-206 ◽  
Author(s):  
R. J. Plymen
Keyword(s):  
Character Formula ◽  
Weyl Character Formula

Tokuyama’s Theorem

2011 ◽  
Author(s):  
Ben Brubaker ◽  
Daniel Bump ◽  
Solomon Friedberg
Keyword(s):  
Eisenstein Series ◽  
Whittaker Function ◽  
Character Formula ◽  
Schur Polynomials ◽  
Normalization Constant ◽  
Small Letter ◽  
Weyl Character Formula

This chapter introduces the Tokuyama's Theorem, first by writing the Weyl character formula and restating Schur polynomials, the values of the Whittaker function multiplied by the normalization constant. The λ‎-parts of Whittaker coefficients of Eisenstein series can be profitably regarded as a deformation of the numerator in the Weyl character formula. This leads to deformations of the Weyl character formula. Tokuyama gave such a deformation. It is an expression of ssubscript Greek small letter lamda(z) as a ratio of a numerator to a denominator. The denominator is a deformation of the Weyl denominator, and the numerator is a sum over Gelfand-Tsetlin patterns with top row λ‎ + ρ‎.

Crystals and p-adic Integration

2011 ◽  
Author(s):  
Ben Brubaker ◽  
Daniel Bump ◽  
Solomon Friedberg
Keyword(s):  
Partition Function ◽  
Generating Function ◽  
Whittaker Function ◽  
Character Formula ◽  
Whittaker Functions ◽  
Unipotent Subgroup ◽  
Enveloping Algebra ◽  
Quantized Enveloping Algebra ◽  
Kostant Partition Function ◽  
Weyl Character Formula

This chapter describes the properties of Kashiwara's crystal and its role in unipotent p-adic integrations related to Whittaker functions. In many cases, integrations of representation theoretic import over the maximal unipotent subgroup of a p-adic group can be replaced by a sum over Kashiwara's crystal. Partly motivated by the crystal description presented in Chapter 2 of this book, this perspective was advocated by Bump and Nakasuji. Later work by McNamara and Kim and Lee extended this philosophy yet further. Indeed, McNamara shows that the computation of the metaplectic Whittaker function is initially given as a sum over Kashiwara's crystal. The chapter considers Kostant's generating function, the character of the quantized enveloping algebra, and its association with Kashiwara's crystal, along with the Kostant partition function and the Weyl character formula.

scholarly journals Fundamental weights, permutation weights and Weyl character formula

1999 ◽  
Vol 32 (9) ◽  
pp. 1701-1707 ◽  
Author(s):  
H R Karadayi ◽  
M Gungormez
Keyword(s):  
Character Formula ◽  
Weyl Character Formula

scholarly journals Lie algebra in quantum physics by means of computer algebra

2017 ◽  
Author(s):  
Ichio Kikuchi ◽  
Akihito Kikuchi
Keyword(s):  
Quantum Mechanics ◽  
Angular Momentum ◽  
Lie Algebra ◽  
Computer Algebra ◽  
Quantum Physics ◽  
Character Formula ◽  
Weyl Character Formula ◽  
Weight Modules

This article explains how to apply the computer algebra package GAP (www.gap-system.org) in the computation of the problems in quantum physics, in which the application of Lie algebra is necessary. The article contains several exemplary computations which readers would follow in the desktop PC: such as, the brief review of elementary ideas of Lie algebra, the angular momentum in quantum mechanics, the quark eight-fold-way model, and the usage of Weyl character formula (in order to construct weight modules, and to count correctly the degeneracy

Quantum mechanics and the geometry of the Weyl character formula

1990 ◽  
Vol 337 (2) ◽  
pp. 467-486 ◽  
Author(s):  
Orlando Alvarez ◽  
I.M. Singer ◽  
Paul Windey
Keyword(s):  
Quantum Mechanics ◽  
Character Formula ◽  
Weyl Character Formula

The six-vertex model and deformations of the Weyl character formula

2015 ◽  
Vol 42 (4) ◽  
pp. 917-958 ◽  
Author(s):  
Ben Brubaker ◽  
Andrew Schultz
Keyword(s):  
Character Formula ◽  
Vertex Model ◽  
Weyl Character Formula
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