Partial flag varieties, stable envelopes, and weight functions

  • Richárd Rimányi

    University of North Carolina at Chapel Hill, USA
  • Vitaly Tarasov

    Indiana University Purdue University Indianapolis, USA
  • Alexander Varchenko

    University of North Carolina at Chapel Hill, USA

Abstract

We consider the cotangent bundle of a partial flag variety, , and the torus equivariant cohomology . In [9], a Yangian module structure was introduced on . We identify this Yangian module structure with the Yangian module structure introduced in [5]. This identifies the operators of quantum multiplication by divisors on , described in [9], with the action of the dynamical Hamiltonians from [20], [10], [5]. To construct these identifications we provide a formula for the stable envelope maps, associated with the partial flag varieties and introduced in [9]. The formula is in terms of the Yangian weight functions introduced in [19], c.f. [21], [22], in order to construct q-hypergeometric solutions of qKZ equations.

Cite this article

Richárd Rimányi, Vitaly Tarasov, Alexander Varchenko, Partial flag varieties, stable envelopes, and weight functions. Quantum Topol. 6 (2015), no. 2, pp. 333–364

DOI 10.4171/QT/65