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Pieri algebras for the orthogonal and symplectic groups

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Abstract

We study the structure of a family of algebras which encodes an iterated version of the Pieri Rule for the complex orthogonal group. In particular, we show that each of these algebras has a standard monomial basis and has a flat deformation to a Hibi algebra. There is also a parallel theory for the complex symplectic group.

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Authors and Affiliations

  1. Department of Mathematics, Ewha Womans University, Daehyun-dong Seodaemun-gu, Seoul, 120-750, South Korea

    Sangjib Kim

  2. Department of Mathematics, National University of Singapore, Block S17, 10 Lower Keng Ridge Road, Singapore, 119076, Singapore

    Soo Teck Lee

Authors
  1. Sangjib Kim
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  2. Soo Teck Lee
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Corresponding author

Correspondence to Sangjib Kim.

Additional information

The second named author is partially supported by NUS grant R-146-000-110-112.

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Kim, S., Lee, S.T. Pieri algebras for the orthogonal and symplectic groups. Isr. J. Math. 195, 215–245 (2013). https://doi.org/10.1007/s11856-012-0105-1

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  • DOI: https://doi.org/10.1007/s11856-012-0105-1

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