Characters of Exponential-polynomial Modules

‘SOME REMARKS ON GILL’S THEOREMS ON YOUNG MODULES’ AUTHOR(S): Professor Stephen Donkin Some remarks on Gill’s Theorems on Young Modules

In a recent paper, [2], Gill, using methods of the modular representation theory of finite groups, describes some results on the tensor product of Young modules for symmetric groups. We here give an alternative approach using the polynomial representation theory of general linear groups and the Schur functor. The main result is a formula for the multiplicities of Young modules in a tensor produ...

Fermionic Characters and Arbitrary Highest-weight Integrable Sl R+1 -modules

This paper contains the generalization of the Feigin-Stoyanovsky construction to all integrable sl r+1-modules. We give formulas for the q-characters of any highest-weight integrable module of sl r+1 as a linear combination of the fermionic q-characters of the fusion products of a special set of integrable modules. The coefficients in the sum are the entries of the inverse matrix of generalized...

Exponential polynomials and D-modules

We introduce D-modules adapted to study ideals generated by exponential polynomials. ∗Partially supported by the NSF grants DMS-9000619 and CDR-8803012 †Partially supported by the NSF grant DMS-9000619

A Character Formula for the Category Õ

One may construct, for any function on the integers, an irreducible module of level zero for affine sl(2), using the values of the function as structure constants. The modules constructed using exponential-polynomial functions realise the irreducible modules with finite-dimensional weight spaces in the category Õ of Chari. In this work, an expression for the formal character of such a module is...

Extensions of Baer and quasi-Baer modules