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View all- Desrosiers PLapointe LMathieu P(2018)Classical symmetric functions in superspaceJournal of Algebraic Combinatorics: An International Journal10.1007/s10801-006-0020-924:2(209-238)Online publication date: 27-Dec-2018
A Determinantal Formula for Supersymmetric Schur Polynomials
Pages 283 - 307
Abstract
We derive a new formula for the supersymmetric Schur polynomial sλ(x/y). The origin of this formula goes back to representation theory of the Lie superalgebra gl(m/n). In particular, we show how a character formula due to Kac and Wakimoto can be applied to covariant representations, leading to a new expression for sλ(x/y). This new expression gives rise to a determinantal formula for sλ(x/y). In particular, the denominator identity for gl(m/n) corresponds to a determinantal identity combining Cauchy's double alternant with Vandermonde's determinant. We provide a second and independent proof of the new determinantal formula by showing that it satisfies the four characteristic properties of supersymmetric Schur polynomials. A third and more direct proof ties up our formula with that of Sergeev-Pragacz.
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22. Private communication: This was outlined to us by Alain Lascoux as an advisor of FPSAC2002, where the results of this paper were presented as a talk.
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Copyright © Copyright © 2003 Kluwer Academic Publishers.
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Published: 01 May 2003
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View all- Desrosiers PLapointe LMathieu P(2018)Classical symmetric functions in superspaceJournal of Algebraic Combinatorics: An International Journal10.1007/s10801-006-0020-924:2(209-238)Online publication date: 27-Dec-2018