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- W3170963341 abstract "In this paper, we introduce {it factorial} analogues of the ordinary Hall--Littlewood $P$- and $Q$-polynomials, which we call the {it factorial Hall--Littlewood $P$- and $Q$-polynomials}. Using the {it universal} formal group law, we further generalize these polynomials to the {it universal factorial Hall--Littlewood $P$- and $Q$-functions}. We show that these functions satisfy the {it vanishing property} which the ordinary factorial Schur $S$-, $P$-, and $Q$-polynomials have. By the vanishing property, we derive the Pieri-type formula and a certain generalization of the classical hook formula. We then characterize our functions in terms of Gysin maps from flag bundles in the complex cobordism theory. Using this characterization and Gysin formulas for flag bundles, we can obtain generating functions for the universal factorial Hall--Littlewood $P$- and $Q$-functions. Using our generating functions, we can show that our factorial Hall--Littlewood $P$- and $Q$-polynomials have a certain {it cancellation property}. Further applications such as Pfaffian formulas for $K$-theoretic factorial $Q$-polynomials are also given." @default.
- W3170963341 created "2021-06-22" @default.
- W3170963341 creator A5026028445 @default.
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- W3170963341 date "2017-05-13" @default.
- W3170963341 modified "2023-09-23" @default.
- W3170963341 title "The universal factorial Hall-Littlewood $P$- and $Q$-functions" @default.
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- W3170963341 doi "https://doi.org/10.48550/arxiv.1705.04791" @default.
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