Equivariant Cohomology of Weighted Grassmannians and Weighted Schubert Classes

Abstract

In this paper, we study the T_w-equivariant cohomology of the weighted Grassmannians wGr(d,n) introduced by Corti-Reid where T_w is the n-dimensional torus that naturally acts on wGr(d,n). We introduce the equivariant weighted Schubert classes and, after we show that they form a basis of the equivariant cohomology, we give an explicit formula for the structure constants with respect to this Schubert basis. We also find a linearly independent subset {wu_1,...,wu_n} of Lie(T_w)^* such that those structure constants are polynomials in wu_i's with non-negative coefficients, up to a permutation on the weights.

17 pages. Comments are welcome

References in corpus (3)

• Hamiltonian group actions on symplectic Deligne-Mumford stacks and toric orbifolds
• Equivariant geometry and the cohomology of the moduli space of curves
• Moment Angle Complexes and Big Cohen-Macaulayness

Cited by in corpus (1)

• Schur polynomials and Weighted Grassmannians