TY - CHAP
T1 - Universal gysin formulas for the universal hall-littlewood functions
AU - Nakagawa, Masaki
AU - Naruse, Hiroshi
N1 - Funding Information:
55N22, 57R77. Key words and phrases. Schur S-, P-, and Q-functions, Hall-Littlewood function, complex-oriented generalized cohomology theory, Gysin map. The first author is partially supported by the Grant-in-Aid for Scientific Research (C) 15K04876, Japan Society for the Promotion of Science. The second author is partially supported by the Grant-in-Aid for Scientific Research (B) 16H03921, Japan Society for the Promotion of Science.
Publisher Copyright:
©2018 American Mathematical Society.
PY - 2018
Y1 - 2018
N2 - 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 universal analogue of the Hall-Littlewood polynomials, which we call the universal Hall-Littlewood functions, and give Gysin formulas for various flag bundles in the complex cobordism theory. Furthermore, we give two kinds of the universal analogue of the Schur polynomials, and some Gysin formulas for these functions are established.
AB - 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 universal analogue of the Hall-Littlewood polynomials, which we call the universal Hall-Littlewood functions, and give Gysin formulas for various flag bundles in the complex cobordism theory. Furthermore, we give two kinds of the universal analogue of the Schur polynomials, and some Gysin formulas for these functions are established.
KW - Complex-oriented generalized cohomology theory
KW - Gysin map
KW - Hall-Littlewood function
KW - Schur S-, P- and Q-functions
UR - http://www.scopus.com/inward/record.url?scp=85049961060&partnerID=8YFLogxK
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U2 - 10.1090/conm/708/14267
DO - 10.1090/conm/708/14267
M3 - Chapter
AN - SCOPUS:85049961060
T3 - Contemporary Mathematics
SP - 201
EP - 244
BT - Contemporary Mathematics
PB - American Mathematical Society
ER -