Schur Polynomials and $$\mathrm{GL}(n, \mathbb{C})$$

2013 ◽  
pp. 379-385
Author(s):  
Daniel Bump
Keyword(s):  
Schur Polynomials

PHASE CONDITIONS FOR SCHUR POLYNOMIALS

2002 ◽  
Vol 35 (1) ◽  
pp. 187-191 ◽  
Author(s):  
L.H. Keel ◽  
S.P. Bhattacharyya
Keyword(s):  
Schur Polynomials

scholarly journals Symmetric Functions for the Generating Matrix of the Yangian of $\mathfrak{gl}_n({\Bbb C})$

10.37236/217 ◽  
2009 ◽  
Vol 16 (1) ◽  
Author(s):  
Natasha Rozhkovskaya
Keyword(s):  
Symmetric Functions ◽  
Combinatorial Identities ◽  
Schur Polynomials ◽  
Generating Matrix

Analogues of classical combinatorial identities for elementary and homogeneous symmetric functions with coefficients in the Yangian are proved. As a corollary, similar relations are deduced for shifted Schur polynomials.

scholarly journals Drinfeld-Sokolov Hierarchies, Tau Functions, and Generalized Schur Polynomials

2018 ◽  
Author(s):  
Mattia Cafasso ◽  
◽  
Ann du Crest de Villeneuve ◽  
Di Yang ◽  
◽  
...  
Keyword(s):  
Schur Polynomials ◽  
Tau Functions

scholarly journals Invariant valuations on quaternionic vector spaces

2012 ◽  
Vol 11 (3) ◽  
pp. 467-499 ◽  
Author(s):  
Andreas Bernig
Keyword(s):  
Vector Space ◽  
Vector Spaces ◽  
Young Diagrams ◽  
Schur Polynomials ◽  
Combinatorial Dimension ◽  
Translation Invariant

AbstractThe spaces of Sp(n)-, Sp(n) · U(1)- and Sp(n) · Sp(1)-invariant, translation-invariant, continuous convex valuations on the quaternionic vector space ℍn are studied. Combinatorial dimension formulae involving Young diagrams and Schur polynomials are proved.

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.

scholarly journals Exact results and Schur expansions in quiver Chern-Simons-matter theories

2020 ◽  
Vol 2020 (10) ◽  
Author(s):  
Leonardo Santilli ◽  
Miguel Tierz
Keyword(s):  
Simons Theory ◽  
Partition Functions ◽  
Wilson Loops ◽  
Model Formulation ◽  
Schur Polynomials ◽  
Three Sphere ◽  
The Matrix ◽  
The Masses ◽  
Chern Simons ◽  
Chern Simons Theory

Abstract We study several quiver Chern-Simons-matter theories on the three-sphere, combining the matrix model formulation with a systematic use of Mordell’s integral, computing partition functions and checking dualities. We also consider Wilson loops in ABJ(M) theories, distinguishing between typical (long) and atypical (short) representations and focusing on the former. Using the Berele-Regev factorization of supersymmetric Schur polynomials, we express the expectation value of the Wilson loops in terms of sums of observables of two factorized copies of U(N ) pure Chern-Simons theory on the sphere. Then, we use the Cauchy identity to study the partition functions of a number of quiver Chern-Simons-matter models and the result is interpreted as a perturbative expansion in the parameters tj = −e2πmj , where mj are the masses. Through the paper, we incorporate different generalizations, such as deformations by real masses and/or Fayet-Iliopoulos parameters, the consideration of a Romans mass in the gravity dual, and adjoint matter.

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