arXiv subjects

William J. Cook

Publications and source records attributed to William J. Cook.

3 recordsLinked to original sources

arXiv2009

On a symmetry of the category of integrable modules

Haisheng Li showed that given a module (W,Y_W(\cdot,x)) for a vertex algebra (V,Y(\cdot,x)), one can obtain a new V-module W^Δ = (W,Y_W(Δ(x)\cdot,x)) if Δ(x) satisfies certain natural conditions. Li presented a collection of such Δ-operators for V=L(k,0) (a vertex operator algebra associated with an affine Lie algebras, k a positive integer). In this paper, for each irreducible L(k,0)-module W, we find a highest weight vector of W^Δ when Δis associated with a miniscule coweight. From this we completely determine the action of these Δ-operators on the set of isomorphism equivalence classes of L(k,0)-modules.

math.QA↗

arXiv2006

A recurrence relation for characters of highest weight integrable modules for affine Lie algebras

Using certain results for the vertex operator algebras associated with affine Lie algebras we obtain recurrence relations for the characters of integrable highest weight irreducible modules for an affine Lie algebra. As an application we show that in the simply-laced level 1 case, these recurrence relations give the known characters, whose principal specializations naturally give rise to some multisum Macdonald identities.

math.QA↗

arXiv2005

On the Constructive Inverse Problem in Differential Galois Theory

We give sufficient conditions for a linear differential equation to have a given semisimple group as its Galois group. For any linear algebraic group G given as a semidirect product of a finite subgroup and a normal subgroup that is a product of groups of type An, Cn, Dn, E6, or E7, we construct a differential equation over C(x) having Galois group G.

math.GM↗