Traces, Schubert calculus, and Hochschild cohomology of category $\mathcal{O}$
Abstract
We discuss how the Hochschild cohomology of a dg category can be computed as the trace of its Serre functor. Applying this approach to the principal block of the BernsteinGelfandGelfand category $\mathcal{O}$, we obtain its Hochschild cohomology as the compactly supported cohomology of an associated space. Equivalently, writing $\mathcal{O}$ as modules over the endomorphism algebra $A$ of a minimal projective generator, this is the Hochschild cohomology of $A$. In particular our computation gives the Euler characteristic of the Hochschild cohomology of $\mathcal{O}$ in type A.
 Publication:

arXiv eprints
 Pub Date:
 December 2020
 arXiv:
 arXiv:2012.02744
 Bibcode:
 2020arXiv201202744K
 Keywords:

 Mathematics  Representation Theory;
 Mathematics  Algebraic Geometry
 EPrint:
 9 pages