DOAJ
Open Access
2014
Chevalley-Monk and Giambelli formulas for Peterson Varieties
Elizabeth Drellich
Abstrak
A Peterson variety is a subvariety of the flag variety $G/B$ defined by certain linear conditions. Peterson varieties appear in the construction of the quantum cohomology of partial flag varieties and in applications to the Toda flows. Each Peterson variety has a one-dimensional torus $S^1$ acting on it. We give a basis of Peterson Schubert classes for $H_{S^1}^*(Pet)$ and identify the ring generators. In type A Harada-Tymoczko gave a positive Monk formula, and Bayegan-Harada gave Giambelli's formula for multiplication in the cohomology ring. This paper gives a Chevalley-Monk rule and Giambelli's formula for all Lie types.
Topik & Kata Kunci
Penulis (1)
E
Elizabeth Drellich
Akses Cepat
Informasi Jurnal
- Tahun Terbit
- 2014
- Sumber Database
- DOAJ
- DOI
- 10.46298/dmtcs.2449
- Akses
- Open Access ✓