The Grothendieck ring of the periplectic Lie supergroup and supersymmetric functions

2019/11/22 by Im, Mee Seong, Reif, Shifra, Serganova, Vera
#FOS: Mathematics #Representation Theory (math.RT)

paper · doi:10.48550/arxiv.1911.12301

Abstract

We show that the Grothendieck ring of finite-dimensional representations of the periplectic Lie supergroup P(n) is isomorphic to the ring of symmetric polynomials in x₁^{± 1}, …, x_n^{± 1} whose evaluation x₁=x₂^-1=t is independent of t.

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• Grothendieck rings of periplectic Lie superalgebras
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• Grothendieck rings of basic classical Lie superalgebras
• Stable Higher Specht Polynomials and Representations of Infinite Symmetric Groups
• Polynomialité d'anneaux de représentations modulaires projectives