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A New Q-Selberg Integral, Schur Functions, And Young Books

J. Kim, S. Okada
Published 2014 · Mathematics

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Recently, Kim and Oh expressed the Selberg integral in terms of the number of Young books which are a generalization of standard Young tableaux of shifted staircase shape. In this paper the generating function for Young books according to major index statistic is considered. It is shown that this generating function can be written as a Jackson integral which gives a new q-Selberg integral. It is also shown that the new q-Selberg integral has an expression in terms of Schur functions.
This paper references
10.1007/S11139-005-4849-7
q-Selberg Integrals and Macdonald Polynomials
S. Warnaar (2005)
10.1016/0001-8708(89)90004-2
On the decomposition of tensor products of the representations of the classical groups: By means of the universal characters
K. Koike (1989)
10.1017/CBO9780511609589
Enumerative Combinatorics: Index
R. Stanley (1999)
10.1007/978-4-431-54270-4_5
From Palev’s Study of Wigner Quantum Systems to New Results on Sums of Schur Functions
R. King (2013)
10.1137/0519067
A proof of Askey's conjectured q-analogue of Selberg's integral and a conjecture of Morris
Kevin W. J. Kadell (1988)
10.1007/S10801-010-0221-0
(q,t)-Deformations of multivariate hook product formulae
S. Okada (2009)
10.1017/CBO9781139058520
Enumerative Combinatorics by Richard P. Stanley
R. P. Stanley (2011)
10.1137/0511084
Some Basic Hypergeometric Extensions of Integrals of Selberg and Andrews
R. Askey (1980)
10.1090/chel/357
The Theory of Group Characters and Matrix Representations of Groups
D. E. Littlewood (2006)
S - functions and characters of Lie algebras and superalgebras In D
R. King (1989)
Enumerative Combinatorics Vol
R. P. Stanley (2011)
Une q-intégrale de Selberg–Askey
L. Habsieger (1988)
10.1515/9783111548050-028
Q
Chlorpromazine Thorazine (1824)
10.1090/S0273-0979-08-01221-4
The importance of the Selberg integral
P. Forrester (2007)
10.1137/0519111
A q-integral of Selberg and Askey
L. Habsieger (1988)
10.1137/0519066
A Proof of Some q-Analogues of Selberg’s Integral for $k=1$
Kevin W. J. Kadell (1988)
Remarks on a multiple integral
A. Selberg (1944)
Permutohedra
A. Postnikov (2009)
10.1093/IMRN/RNN153
Permutohedra, Associahedra, and Beyond
A. Postnikov (2005)
Symmetric functions and Hall polynomials
I. MacDonald (1979)
10.24033/ASENS.1749
$q$-Selberg integrals and Macdonald polynomials
J. Kaneko (1996)
On Representations of Classical Groups over Finite Local Rings of Length Two
Pooja Singla (2011)



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