Cherednik algebras and subspace arrangementsAlgebra & Discrete Mathematics
|José Simental Rodríguez, UC Davis
|Mon, Dec 10 2018, 11:00AM
For fixed e and n, we consider the set of points in C^n that have some e coordinates equal. This is a subspace arrangement, whose defining ideal has been studied from the point of view of combinatorial commutative algebra. This ideal turns out to be a module over the type A rational Cherednik algebra (with parameter 1/e). I will explain joint work with C. Bowman and E. Norton, that confirms a conjecture of Berkesch-Griffeth-Sam by constructing a resolution of the e-equals ideal by standard modules. Forgetting the action of the Cherednik algebra, this gives a minimal graded-free resolution of the ideal, thus providing formulas (given in terms of abacus combinatorics) for interesting homological invariants, such as the Hilbert series and the Castelnuovo-Mumford regularity. Time permitting, I will explain how to generalize this to slightly more general subspace arrangements. No prior knowledge of Cherednik algebras will be assumed.