2021/02/22 by Kowalenko, Ethan, Mautner, Carl
#16S37 #52C40 #Combinatorics (math.CO) #FOS: Mathematics #Representation Theory (math.RT)
paper · doi:10.48550/arxiv.2102.11320
We associate to a sufficiently generic oriented matroid program and choice of linear system of parameters a finite dimensional algebra, whose representation theory is analogous to blocks of Bernstein--Gelfand--Gelfand category \mathcal O. When the data above comes from a generic linear program for a hyperplane arrangement, we recover the algebra defined by Braden--Licata--Proudfoot--Webster. Applying our construction to nonlinear oriented matroid programs provides a large new class of algebras. For Euclidean oriented matroid programs, the resulting algebras are quasi-hereditary and Koszul, as in the linear setting. In the non-Euclidean case, we obtain algebras that are not quasi-hereditary and not known to be Koszul, but still have a natural class of standard modules and satisfy numerical analogues of quasi-heredity and Koszulity on the level of graded Grothendieck groups.