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.

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

UR - http://www.scopus.com/inward/citedby.url?scp=85049961060&partnerID=8YFLogxK

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 -