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Cherednik algebras and subspace arrangements

Algebra & Discrete Mathematics

Speaker: José Simental Rodríguez, UC Davis
Location: 2112 MSB
Start time: 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.