Quantum groups, quantum tori, and the Grothendieck-Springer resolution

2015/08/28 by Schrader, Gus, Shapiro, Alexander
#FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #Quantum Algebra (math.QA) #Representation Theory (math.RT)

paper · doi:10.48550/arxiv.1508.07057

Abstract

We construct an algebra embedding of the quantum group U_q(\mathfrakg) into the quantum coordinate ring O_q[G^w₀,w₀/H] of the reduced big double Bruhat cell in G. This embedding factors through the Heisenberg double H_q of the quantum Borel subalgebra U_≥0, which we relate to O_q[G] via twisting by the longest element of the quantum Weyl group. Our construction is inspired by the Poisson geometry of the Grothendieck-Springer resolution studied by Evens and Lu, and the quantum Beilinson-Bernstein theorem investigated by Backelin, Kremnitzer, and Tanisaki.

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