Soichi OKADA: Young books and \(q\)-Selberg integrals

Kim and Oh introduced the notion of Young books as a generalization of standard Young tableaux of shifted staircase shape, and expressed the number of Young books in terms of the Selberg integral. In this talk, we consider the generating function for Young books according to major index statistic, and show that it can be written as a new \(q\)-Selberg integral. Also we present the evaluations of several variants of the \(q\)-Selberg integral by means of the Cauchy-type identities for classical group characters. This talk is based on a joint work with Jang Soo Kim.