Speaker: Dr. Seung-IL Choi(Seoul National Univ.)
Date: May 24. Thursday 16:30 - 17:30
Room: AORC Seminar Room (General Studies, 기초학문관 3층)
Title: Product of two Schur $P$-functions and staircase skew Schur functions
Abstract:
In this talk we give new characterizations of structure constants of
the expansions of product of two Schur $P$-functions and s taircase skew Schur functions in the Schur $P$ basis.
There were well-known results about these nonnegative integer constants.
In 1989, Stembridge provided a combinatorial description of the constants in the first expansion,
which is in terms of marked shifted tableaux. We here yield an alternative description of it in terms of shifted tableaux with double alphabets.
In 2012, Ardila-Serrano and Dewitt gave separately answers to the question raised by Stanley that
what kinds of skew Schur functions are elements the subring $\Omega$ of the ring of symmetric functions $\Lambda$.
Schur functions of staircase skew shape or its rotated shape are nonnegative integral sums of Schur $P$-functions.
By using the theory of $\mathfrak{q}(n)$-crystal basis we gave an alternative description of the constants in the second expansion