Skein Modules from Skew Howe Duality and Affine Extensions

Categorical Geometric Skew Howe Duality

We categorify the R-matrix isomorphism between tensor products of minuscule representations of Uq(sln) by constructing an equivalence between the derived categories of coherent sheaves on the corresponding convolution products in the affine Grassmannian. The main step in the construction is a categorification of representations of Uq(sl2) which are related to representations of Uq(sln) by quant...

On Duality for Skew Field Extensions

In this paper a duality principle is formulated for statements about skew field extensions of finite (left or right) degree. A proof for this duality principle is given by constructing for every extension L/K of finite degree a dual extension LJK, . These dual extensions are constructed by embedding a given L/K in an inner Galois extension N/K. The Appendix shows that such an embedding can alwa...

On skew Armendariz and skew quasi-Armendariz modules

Let $alpha$ be an endomorphism and $delta$ an $alpha$-derivationof a ring $R$.  In this paper we  study the relationship between an$R$-module $M_R$ and the  general polynomial module  $M[x]$ over theskew polynomial ring $R[x;alpha,delta]$. We introduce the notionsof skew-Armendariz modules and skew quasi-Armendariz modules whichare generalizations of $alpha$-Armendariz modules and extend thecla...

Howe Duality for Lie Superalgebras

We study a dual pair of general linear Lie superalgebras in the sense of R. Howe. We give an explicit multiplicity-free decomposition of a symmetric and skew-symmetric algebra (in the super sense) under the action of the dual pair and present explicit formulas for the highest weight vectors in each isotypic subspace of the symmetric algebra. We give an explicit multiplicity-free decomposition i...

Extensions of Baer and quasi-Baer modules