Publication

The Center of Small Quantum Groups I: The Principal Block in Type A

Anna Lachowska
2018
Journal Articles

Abstract

We develop an elementary algebraic method to compute the center of the principal block of a small quantum group associated with a complex semisimple Lie algebra at a root of unity. The cases of sl(3) and sl(4) are computed explicitly. This allows us to formulate the conjecture that, as a bigraded vector space, the center of a regular block of the small quantum sl(m) at a root of unity is isomorphic to Haiman's diagonal coinvariant algebra for the symmetric group S-m.

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The Center of Small Quantum Groups I: The Principal Block in Type A

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