Quantum cohomology and the Satake isomorphism

Details Quantum cohomology and the Satake isomorphism Quantum cohomology and the Satake isomorphism

2011-06-15

arxiv.org/abs/1106.3120v1

Mathematics

Algebraic Geometry

Scientific paper

We prove that the geometric Satake correspondence admits quantum corrections for minuscule Grassmannians of Dynkin types $A$ and $D$. We find, as a corollary, that the quantum connection of a spinor variety $OG(n,2n)$ can be obtained as the half-spinorial representation of that of the quadric $Q_{2n-2}$. We view the (quantum) cohomology of these Grassmannians as endowed simultaneously with two structures, one of a module over the algebra of symmetric functions, and the other, of a module over the Langlands dual Lie algebra, and investigate the interaction between the two. In particular, we study primitive classes $y$ in the cohomology of a minuscule Grassmannian $G/P$ that are characterized by the condition that the operator of cup product by $y$ is in the image of the Lie algebra action. Our main result states that quantum correction preserves primitivity. We provide a quantum counterpart to a result obtained by V. Ginzburg in the classical setting by giving explicit formulas for the quantum corrections to homogeneous primitive elements.

Affiliated with

Also associated with

No associations

Rating

Quantum cohomology and the Satake isomorphism 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 Quantum cohomology and the Satake isomorphism, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Quantum cohomology and the Satake isomorphism will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-189291