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Lie Groups and Representation Theory Seminar

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Place: Usually Room 126 (this year)
Graduate School of Mathematical Sciences, the University of Tokyo [ Access ]
Date: March 24 (Tue), 2015, 18:00-19:30
Place: Room 126, Graduate School of Mathematical Sciences, the University of Tokyo
Speaker: Piotr Pragacz (Institute of Mathematics, Polish Academy of Sciences)
Title: A Gysin formula for Hall-Littlewood polynomials
[ pdf ]
Schubert calculus on Grassmannians is governed by Schur S- functions, the one on Lagrangian Grassmannians by Schur Q-functions. There were several attempts to give a unifying approach to both situations. We propose to use Hall-Littlewood symmetric polynomials. They appeared implicitly in Hall's study of the combinatorial lattice structure of finite abelian p-groups and in Green's calculations of the characters of GL(n) over finite fields; they appeared explicitly in the work of Littlewood on some problems in representation theory. With the projection in a Grassmann bundle, there is associated its Gysin map, induced by pushing forward cycles (topologists call it "integration along fibers"). We state and prove a Gysin formula for HL-polynomials in these bundles. We discuss its two specializations, giving better insights to previously known formulas for Schur S- and P-functions.

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