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q-Identities and Affinized Projective Varieties¶II. Flag Varieties

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Abstract:

In a previous paper we defined the concept of an affinized projective variety and its associated Hilbert series. We computed the Hilbert series for varieties associated to quadratic monomial ideals. In this paper we show how to apply these results to affinized flag varieties. We discuss various examples and conjecture a correspondence between the Hilbert series of an affinized flag variety and a modified Hall–Littlewood polynomial. We briefly discuss the application of these results to quasi-particle character formulas for affine Lie algebra modules.

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Authors and Affiliations

  1. Department of Physics and Mathematical Physics, University of Adelaide, Adelaide SA 5005, Australia. E-mail: pbouwkne@physics.adelaide.edu.au, , , , , , AU

    Peter Bouwknegt & Nick Halmagyi

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  1. Peter Bouwknegt
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  2. Nick Halmagyi
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Received: 16 March 1999 / Accepted: 15 October 1999

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Bouwknegt, P., Halmagyi, N. q-Identities and Affinized Projective Varieties¶II. Flag Varieties. Comm Math Phys 210, 663–684 (2000). https://doi.org/10.1007/s002200050795

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  • DOI: https://doi.org/10.1007/s002200050795

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