The Ramanujan Journal

, Volume 42, Issue 1, pp 43–57 | Cite as

A new q-Selberg integral, Schur functions, and Young books

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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.

Keywords

q-Selberg integral Schur functions Young books  P-Partitions 

Mathematics Subject Classification

05A15 05E05 33D05 
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Notes

Acknowledgments

The authors would like to thank Ole Warnaar for helpful comments.

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Copyright information

© Springer Science+Business Media New York 2015

Authors and Affiliations

  1. 1.Department of MathematicsSungkyunkwan UniversitySuwonSouth Korea
  2. 2.Graduate School of MathematicsNagoya UniversityNagoyaJapan

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