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arXiv · 1604.00451

Universal Gysin formulas for the universal Hall-Littlewood functions

Masaki Nakagawa·Hiroshi Naruse
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Abstract

It is known that the usual Schur $S$- and $P$-polynomials can be described via the Gysin homomorphisms for flag bundles in the ordinary cohomology theory. Recently, P. Pragacz generalized these Gysin formulas to the Hall-Littlewood polynomials. In this paper, we introduce a {\it universal} analogue of the Hall-Littlewood polynomials, which we call the {\it universal Hall-Littlewood functions}, and give Gysin formulas for various flag bundles in the complex cobordism theory. Furthermore, we give two kinds of the {\it universal} analogue of the schur polynomials, and some Gysin formulas for these functions are established.

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Masaki Nakagawa, Hiroshi Naruse. 2016-04-02. Universal Gysin formulas for the universal Hall-Littlewood functions. https://doi.org/10.1090/conm%2F708%2F14267

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