91 citations · 871 across the 69 of their papers we have counts for
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Equivariant quantum differential equation, Stokes bases, and K-theory for a projective space
Vitaly Tarasov, Alexander Varchenko
We consider the equivariant quantum differential equation for the projective space . We prove an equivariant gamma theorem for , which describes the asymptotics o…
-Hypergeometric solutions of quantum differential equations, quantum Pieri rules, and Gamma theorem
Vitaly Tarasov, Alexander Varchenko
We describe \,-hypergeometric solutions of the equivariant quantum differential equations and associated qKZ difference equations for the cotangent bundle of a partial…
Elliptic and K-theoretic stable envelopes and Newton polytopes
R. Rimányi, V. Tarasov, A. Varchenko
In this paper we consider the cotangent bundles of partial flag varieties. We construct the -theoretic stable envelopes for them and also define a version of the elliptic stable…
Trigonometric weight functions as K-theoretic stable envelope maps for the cotangent bundle of a flag variety
R. Rimanyi, V. Tarasov, A. Varchenko
We consider the cotangent bundle of a partial flag variety, , , and the torus $T=(\C^\times)^{n+1}$ equivariant K-theory algebra $…
Spaces of quasi-exponentials and representations of the Yangian Y(gl_N)
E. Mukhin, V. Tarasov, A. Varchenko
We consider a tensor product $V(b)= \otimes_{i=1}^n\C^N(b_i)$ of the Yangian evaluation vector representations. We consider the action of the commutative Bethe subalgebra…
Hypergeometric solutions of the quantum differential equation of the cotangent bundle of a partial flag variety
V. Tarasov, A. Varchenko
We describe hypergeometric solutions of the quantum differential equation of the cotangent bundle of a gl_n partial flag variety. These hypergeometric solutions manifest the Landau…
Partial flag varieties, stable envelopes and weight functions
R. Rimanyi, V. Tarasov, A. Varchenko
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],…
Quantum cohomology of the cotangent bundle of a flag variety as a Yangian Bethe algebra
V. Gorbounov, R. Rimanyi, V. Tarasov +1
We interpret the equivariant cohomology algebra H^*_{GL_n\times\C^*}(T^*F_λ;\C) of the cotangent bundle of a partial flag variety F_λparametrizing chains of subspaces 0=F_0\subset…
Cohomology classes of conormal bundles of Schubert varieties and Yangian weight functions
R. Rimanyi, V. Tarasov, A. Varchenko
We consider the conormal bundle of a Schubert variety in the cotangent bundle of the Grassmannian of -planes in . This conormal bundle has a fundamental…
The B. and M. Shapiro conjecture in real algebraic geometry and the Bethe ansatz
E. Mukhin, V. Tarasov, A. Varchenko
We prove the B. and M. Shapiro conjecture that says that if the Wronskian of a set of polynomials has real roots only, then the complex span of this set of polynomials has a basis…