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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 |

Abstract: [ 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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