Discrete analogues of Macdonald-Mehta integrals

TL;DR: The reflection groups and coxeter groups is universally compatible with any devices to read and is available in the digital library an online access to it is set as public so you can download it instantly.

TL;DR: Researchers establish a combinatorial skew Howe duality for dual pairs of Lie groups, interpreting it as lattice paths on lozenge tilings, and derive determinant and product formulas for representation multiplicities, with q-analogs and limit shapes of Young diagrams.

TL;DR: Researchers provide a combinatorial proof of Baik-Rains' result on last passage percolation in a quarter square, showing it decomposes into simpler series, and derive GOE^2 fluctuations for iid geometric weights in the large n limit.

TL;DR: In this article , the authors consider the decomposition into irreducible components of the exterior algebra (cid:86) √ cid:16) C n ⊗ (cID:0) C k √ q √ n √ k ∆ ∆) ∆, and derive the limit shape and prove the central limit theorem for the ∆-Krawtchouk polynomial ensemble when n, k tend to infinity and q tends to one at comparable rates.

TL;DR: In this paper, Semisimple Lie Algebras and root systems are used for representation theory, isomorphism and conjugacy theorem, and existence theorem for representation.

TL;DR: In this article, the Askey-Wilson q-beta integral and some associated formulas were used to generate bilinear generating functions for basic orthogonal polynomials.

TL;DR: This volume represents a series of lectures which aims to introduce the beginner to the finite dimensional representations of Lie groups and Lie algebras.

TL;DR: In this article, a classification of finite and affine reflection groups is presented, including Coxeter groups, Hecke algebras and Kazhdan-Lusztig polynomials.