Deformation of Weyl Modules and Generalized Parking Functions

Abstract

Local Weyl modules over two-dimensional currents with values in Glr are deformed into spaces with bases related to parking functions. Using this construction, we (1) propose a simple proof that dimension of the space of diagonal coinvariants is not less than the number of parking functions; (2) describe the limits of Weyl modules in terms of semi-infinite forms and find the limits of characters; and (3) propose a lower bound and state a conjecture for dimensions of Weyl modules with arbitrary highest weights. Also we express characters of deformed Weyl modules in terms of ρ-parking functions and the Frobenius characteristic map.