Partial flag varieties, stable envelopes and weight functions
Abstract
We consider the cotangent bundle T^*F_\lambda of a GL_n partial flag variety, \lambda = (\lambda_1,...,\lambda_N), |\lambda|=\sum_i\lambda_i=n, and the torus T=(C^*)^{n+1} equivariant cohomology H^*_T(T^*F_\lambda). In [MO], a Yangian module structure was introduced on \oplus_{|\lambda|=n} H^*_T(T^*F_\lambda). We identify this Yangian module structure with the Yangian module structure introduced in [GRTV]. This identifies the operators of quantum multiplication by divisors on H^*_T(T^*F_\lambda), described in [MO], with the action of the dynamical Hamiltonians from [TV2, MTV1, GRTV]. To construct these identifications we provide a formula for the stable envelope maps, associated with the partial flag varieties and introduced in [MO]. The formula is in terms of the Yangian weight functions introduced in [TV1], c.f. [TV3, TV4], in order to construct q-hypergeometric solutions of qKZ equations.
Keywords
Cite
@article{arxiv.1212.6240,
title = {Partial flag varieties, stable envelopes and weight functions},
author = {R. Rimanyi and V. Tarasov and A. Varchenko},
journal= {arXiv preprint arXiv:1212.6240},
year = {2013}
}
Comments
Latex, 22 pages, misprints corrected, Section 7.4 edited