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 q-Selberg integral. It is also shown that the new q-Selberg integral has an expression in terms of Schur functions.
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The authors would like to thank Ole Warnaar for helpful comments.
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The first author was partially supported by the TJ Park Science Fellowship of POSCO TJ Park Foundation. The second author was partially supported by the JSPS Grants-in-Aid for Scientific Research No. 24340003.
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Kim, J.S., Okada, S. A new q-Selberg integral, Schur functions, and Young books. Ramanujan J 42, 43–57 (2017). https://doi.org/10.1007/s11139-015-9721-9
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DOI: https://doi.org/10.1007/s11139-015-9721-9