Alexander Braverman

Instanton counting via affine Lie algebras II: From Whittaker vectors to the Seiberg-Witten prepotential

Let G be a simple simply connected algebraic group over ℂ with Lie algebra ( mathfrak{g} ) . Given a parabolic subgroup P ⊂ G, in tikya[1] the first author introduced a certain generating function Z G,P aff . Roughly speaking, these functions count (in a certain sense) framed G-bundles on ℙ2 together with a P-structure on a fixed (horizontal) line in ℙ2. When P = B is a Borel subgroup, the function Z G,B aff was identified in tikya[1] with the Whittaker matrix coefficient in the universal Verma module over the affine Lie algebra ( overset{lower0.5emhbox{

Uhlenbeck Spaces via Affine Lie Algebras

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A finite analog of the AGT relation I: finite W-algebras and quasimaps' spaces

}}{mathfrak{g}} _{aff} ) (here we denote by ( mathfrak{g}_{aff} ) the affinization of ( mathfrak{g} ) and by ( overset{lower0.5emhbox{

Weyl modules and q-Whittaker functions

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Semi-infinite Schubert varieties and quantum K -theory of flag manifolds

}}{mathfrak{g}} _{aff} ) the Lie algebra whose root system is dual to that of ( mathfrak{g}_{aff} ) ).

Iwahori–Hecke algebras for p-adic loop groups

Let G be an almost simple simply connected group over ℂ, and let Bun G a (ℙ2, ℙ1) be the moduli scheme of principalG-bundles on the projective plane ℙ2, of second Chern class a, trivialized along a line ℙ1 ⊂ ℙ2.

Twisted zastava and q-Whittaker functions

Recently Alday, Gaiotto and Tachikawa [2] proposed a conjecture relating 4-dimensional super-symmetric gauge theory for a gauge group G with certain 2-dimensional conformal field theory. This conjecture implies the existence of certain structures on the (equivariant) intersection cohomology of the Uhlenbeck partial compactification of the moduli space of framed G-bundles on

CARTAN DECOMPOSITION FOR COMPLEX LOOP GROUPS

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