### 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 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.

Original language | English |
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Title of host publication | Contemporary Mathematics |

Publisher | American Mathematical Society |

Pages | 201-244 |

Number of pages | 44 |

Volume | 708 |

DOIs | |

Publication status | Published - Jan 1 2018 |

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### Keywords

- Complex-oriented generalized cohomology theory
- Gysin map
- Hall-Littlewood function
- Schur S-, P- and Q-functions

### ASJC Scopus subject areas

- Mathematics(all)

### Cite this

*Contemporary Mathematics*(Vol. 708, pp. 201-244). American Mathematical Society. https://doi.org/10.1090/conm/708/14267

**Universal gysin formulas for the universal hall-littlewood functions.** / Nakagawa, Masaki; Naruse, Hiroshi.

Research output: Chapter in Book/Report/Conference proceeding › Chapter

*Contemporary Mathematics.*vol. 708, American Mathematical Society, pp. 201-244. https://doi.org/10.1090/conm/708/14267

}

TY - CHAP

T1 - Universal gysin formulas for the universal hall-littlewood functions

AU - Nakagawa, Masaki

AU - Naruse, Hiroshi

PY - 2018/1/1

Y1 - 2018/1/1

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

VL - 708

SP - 201

EP - 244

BT - Contemporary Mathematics

PB - American Mathematical Society

ER -