Discrete analogues of Macdonald-Mehta integrals
TL;DR: Close-form product formulas for the (ordinary and signed) enumeration of orthogonal and symplectic tableaux contained in a box are obtained.
read more
About: This article is published in Journal of Combinatorial Theory, Series A. The article was published on 01 Nov 2016. and is currently open access. The article focuses on the topics: Elliptic hypergeometric series & Classical group.
read more
Chat with Paper
AI Agents for this Paper
Find similar papers on Google Scholar, PubMed and Arxiv
Write a critical review of this paper
Analyze citations of this paper to find unaddressed research gaps
Citations
A Nekrasov–Okounkov formula for Macdonald polynomials
Eric M. Rains,S. Ole Warnaar +1 more
TL;DR: In this article, a Macdonald polynomial analogue of the celebrated Nekrasov-Okounkov hook-length formula from the theory of random partitions has been shown to be equivalent to the one of the main conjectures of Hausel and Rodriguez-Villegas.
A Nekrasov-Okounkov formula for Macdonald polynomials
Eric M. Rains,S. Ole Warnaar +1 more
TL;DR: In this article, a Macdonald polynomial analogue of the celebrated Nekrasov-Okounkov hook-length formula from the theory of random partitions has been shown to be equivalent to the one of Hausel and Rodriguez-Villegas.
Evaluation of Binomial Double Sums Involving Absolute Values
TL;DR: Two different proofs of double sums of the form \(\binom {2n}{n+j}\) are provided: one is algorithmic and uses the second author’s computer algebra package Sigma; the second is based on complex contour integrals.
9
Identities from representation theory
Se jin Oh,Travis Scrimshaw +1 more
TL;DR: In this article, a new Jacobi-Trudi-type formula for characters of finite-dimensional irreducible representations in type C n using characters of the fundamental representations and non-intersecting lattice paths was given.
9
•Posted Content
On the combinatorics of last passage percolation in a quarter square and $\mathrm{GOE}^2$ fluctuations
TL;DR: In this paper, it was shown that the generating series for last passage percolation polymers in a point-to-line geometry and in a half-space geometry splits as the product of two simpler generating series.
8
References
•Posted Content
The major index generating function of standard Young tableaux of shapes of the form "staircase minus rectangle"
TL;DR: In this article, a transformation formula for multi-dimensional elliptic hyper-geometric series is used to provide compact, non-determinantal formulae for the generating function with respect to the major index of standard Young tableaux of skew shapes of the form “staircase minus rectangle”.
Correlation Kernels for Discrete Symplectic and Orthogonal Ensembles
Alexei Borodin,Eugene Strahov +1 more
TL;DR: In this paper, Widom derived formulae expressing correlation functions of orthogonal and symplectic ensembles of random matrices in terms of the Meixner and Charlier polynomials.
Minor summation formula of Pfaffians
Masao Ishikawa,Masato Wakayama +1 more
TL;DR: In this paper, a formula involving sub-Pfaffians for a certain weighted sum of minors of an arbitrary given matrix was established, and applied to the generating functions of shifted tableaux.
Orthogonal tableaux and an insertion algorithm for SO (2 n + 1)
TL;DR: These tableaux are used to produce an insertion scheme which gives a combinatorial description of the decomposition of the k th tensor power of the natural action of SO (2 n + 1) into irreducibles.
Odd symplectic groups.
TL;DR: The authors define des groupes symplectiques sur des espaces vectoriels de dimension impaire and define a formule de caracteres for certaines representations tensorielles of ces groupes.