TY - JOUR

T1 - Generating functions for the universal hall-littlewood p- and q-functions

AU - Nakagawa, Masaki

AU - Naruse, Hiroshi

N1 - Publisher Copyright:
Copyright © 2017, The Authors. All rights reserved.
Copyright:
Copyright 2020 Elsevier B.V., All rights reserved.

PY - 2017/5/13

Y1 - 2017/5/13

N2 - Recently, P. Pragacz described the ordinary Hall-Littlewood P-polynomials by means of push-forwards (Gysin maps) from flag bundles in the ordinary cohomol- ogy theory. Together with L. Darondeau, he also gave push-forward formulas (Gysin formulas) for all flag bundles of types A, B, C and D in the ordinary cohomology theory. In this paper, we introduce a generalization of the ordinary Hall-Littlewood P- and Q-polynomials, which we call the universal (factorial) Hall-Littlewood P- and Q-functions, and characterize them in terms of Gysin maps from flag bundles in the complex cobordism theory. We also generalize the (type A) push-forward formula due to Darondeau-Pragacz to the complex cobordism theory. As an application of our Gysin formulas in complex cobordism, we give generating functions for the uni- versal Hall-Littlewood P- and Q-functions and their factorial analogues. Using our generating functions, classical determinantal and Pfaffian formulas for Schur S- and Q-polynomials, and their K-theoretic or factorial analogues can be obtained in a simple and unified manner.MSC Codes 05E05, 14M15, 55N20, 55N22, 57R77

AB - Recently, P. Pragacz described the ordinary Hall-Littlewood P-polynomials by means of push-forwards (Gysin maps) from flag bundles in the ordinary cohomol- ogy theory. Together with L. Darondeau, he also gave push-forward formulas (Gysin formulas) for all flag bundles of types A, B, C and D in the ordinary cohomology theory. In this paper, we introduce a generalization of the ordinary Hall-Littlewood P- and Q-polynomials, which we call the universal (factorial) Hall-Littlewood P- and Q-functions, and characterize them in terms of Gysin maps from flag bundles in the complex cobordism theory. We also generalize the (type A) push-forward formula due to Darondeau-Pragacz to the complex cobordism theory. As an application of our Gysin formulas in complex cobordism, we give generating functions for the uni- versal Hall-Littlewood P- and Q-functions and their factorial analogues. Using our generating functions, classical determinantal and Pfaffian formulas for Schur S- and Q-polynomials, and their K-theoretic or factorial analogues can be obtained in a simple and unified manner.MSC Codes 05E05, 14M15, 55N20, 55N22, 57R77

KW - and Q-functions

KW - Com-plex cobordism theory

KW - Gysin formulas

KW - Hall-Littlewood P- and Q-functions

KW - P-

KW - Schur S-

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M3 - Article

AN - SCOPUS:85095344332

JO - [No source information available]

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SN - 0402-1215

ER -