A new $q$-Selberg integral, Schur functions, and Young books
Jang Soo Kim, Soichi Okada
TL;DR
This paper introduces a new $q$-Selberg integral expressed via Schur functions and Young books, linking combinatorial structures with integral formulas and expanding the understanding of these mathematical objects.
Contribution
It presents a novel $q$-Selberg integral representation related to Young books and Schur functions, extending previous combinatorial and integral identities.
Findings
New $q$-Selberg integral expressed as a Jackson integral
Connection between Young books and Schur functions established
Generating function for Young books related to major index is derived
Abstract
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 -Selberg integral. It is also shown that the new -Selberg integral has an expression in terms of Schur functions.
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Taxonomy
TopicsAdvanced Combinatorial Mathematics · Advanced Mathematical Identities · Random Matrices and Applications