Lachowska, AnnaQi, You2018-12-132018-12-132018-12-132018-10-0110.1093/imrn/rnx062https://infoscience.epfl.ch/handle/20.500.14299/152350WOS:000450254200006We 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.MathematicsMathematicsdiagonal invariantsspringer resolutionquotient ringhopf-algebras3-manifoldscategorificationrepresentationsmodulestext::journal::journal article::research article