2016 Theses Doctoral

# Quantum difference equations for quiver varieties

For an arbitrary Nakajima quiver variety X, we construct an analog of the quantum dynamical Weyl group acting in its equivariant K-theory. The correct generalization of the Weyl group here is the fundamental groupoid of a certain periodic locally finite hyperplane arrangement in Pic(X)⊗C. We identify the lattice part of this groupoid with the operators of quantum difference equation for X. The cases of quivers of finite and affine type are illustrated by explicit examples.

## Files

- Smirnov_columbia_0054D_13250.pdf binary/octet-stream 367 KB Download File

## More About This Work

- Academic Units
- Mathematics
- Thesis Advisors
- Okounkov, Andrei
- Degree
- Ph.D., Columbia University
- Published Here
- April 14, 2016