Quantum Groups and Quantum Cohomology

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In this paper, we study the classical and quantum equivariant cohomology of Nakajima quiver varieties for a general quiver Q.

• Using a geometric R-matrix formalism, we construct a Hopf algebra Y_Q, the Yangian of Q, acting on the cohomology of these varieties, and show several results about their basic structure theory.
• We prove a formula for quantum multiplication by divisors in terms of this Yangian action.
• The quantum connection can be identified with the trigonometric Casimir connection for Y_Q; equivalently, the divisor operators correspond to certain elements of Baxter subalgebras of Y_Q.