Mathematics – Algebraic Geometry
Scientific paper
2011-11-09
Mathematics
Algebraic Geometry
Scientific paper
Let g be a semi-simple Lie algebra. In this paper we study the spaces of based quasi-maps from the projective line P^1 to the flag variety of g (it is well-known that their singularities are supposed to model the singularities of the so called semi-infinite Schubert varieties which are hard to define directly). In the first part of the paper we show that the above spaces are normal and in the case when g is simply laced they are also Gorenstein and have rational singularities. In the second part of the paper we compute the character of the ring of functions on the above spaces; in view of the above results this computation can be thought of as a computation of the (equivariant) K-theoretic J-function of the flag variety of g. We show that when g is simply laced the above characters satisfy the "fermionic recursion" version of the difference quantum Toda lattice (due to B.Feigin, E.Feigin, M.Jimbo, T.Miwa and E.Mukhin). As a byproduct we show that the equivariant K-theoretic J-function of the flag variety of a simply laced Lie algebra g is the universal eigen-function of the difference quantum Toda lattice, thus proving a conjecture of Givental and Lee. Some modification of this result is also shown to hold for non-simply laced g. We also discuss an extension of the above results to the case when g is an affine Lie algebra (this extension is conjectural except when g=sl(N)).
Braverman Alexander
Finkelberg Michael
No associations
LandOfFree
Semi-infinite Schubert varieties and quantum K-theory of flag manifolds does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.
If you have personal experience with Semi-infinite Schubert varieties and quantum K-theory of flag manifolds, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Semi-infinite Schubert varieties and quantum K-theory of flag manifolds will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-43145