Partial flag varieties, stable envelopes and weight functions
arXiv:1212.6240
Abstract
We consider the cotangent bundle T^*F_λof a GL_n partial flag variety, λ= (λ_1,...,λ_N), |λ|=\sum_iλ_i=n, and the torus T=(C^*)^{n+1} equivariant cohomology H^*_T(T^*F_λ). In [MO], a Yangian module structure was introduced on \oplus_{|λ|=n} H^*_T(T^*F_λ). 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_λ), 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.
Latex, 22 pages, misprints corrected, Section 7.4 edited
References in corpus (5)
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- Combinatorial Formulae for Nested Bethe Vectors
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Cited by in corpus (7)
- Combinatorial Formulae for Nested Bethe Vectors
- Trigonometric weight functions as K-theoretic stable envelope maps for the cotangent bundle of a flag variety
- Quantum cohomology of the cotangent bundle of a flag variety as a Yangian Bethe algebra
- Three-Dimensional Mirror Self-Symmetry of the Cotangent Bundle of the Full Flag Variety
- Elliptic Dynamical Quantum Groups and Equivariant Elliptic Cohomology
- Elliptic and K-theoretic stable envelopes and Newton polytopes
- Hypergeometric solutions of the quantum differential equation of the cotangent bundle of a partial flag variety