### 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 |
---|---|

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 |

### Keywords

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

### ASJC Scopus subject areas

- Mathematics(all)

## Fingerprint Dive into the research topics of 'Universal gysin formulas for the universal hall-littlewood functions'. Together they form a unique fingerprint.

## Cite this

Nakagawa, M., & Naruse, H. (2018). Universal gysin formulas for the universal hall-littlewood functions. In

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