Canonical bases in tensor products revisited

Canonical Bases for Fock Spaces and Tensor Products

We relate the canonical basis of the Fock space representation of the quantum affine algebra Uq(ĝln), as defined by Leclerc and Thibon [LT], to the canonical basis of its restriction to Uq(sln), regarded as a based module in the sense of Lusztig. More generally we consider the restriction to any Levi subalgebra. We deduce results on decomposition numbers and branching coefficients of Schur alge...

Tensor product multiplicities, canonical bases and totally positive varieties

Canonical tensor products as a generalization of Gaussian-type orbitals

Fuzzy projective modules and tensor products in fuzzy module categories

Let $R$ be a commutative ring. We write $mbox{Hom}(mu_A, nu_B)$ for the set of all fuzzy $R$-morphisms from $mu_A$ to $nu_B$, where $mu_A$ and $nu_B$ are two fuzzy $R$-modules. We make$mbox{Hom}(mu_A, nu_B)$ into fuzzy $R$-module by redefining a function $alpha:mbox{Hom}(mu_A, nu_B)longrightarrow [0,1]$. We study the properties of the functor $mbox{Hom}(mu_A,-):FRmbox{-Mod}rightarrow FRmbox{-Mo...

On Dual Canonical Bases

The dual basis of the canonical basis of the modified quantized enveloping algebra is studied, in particular for type A. The construction of a basis for the coordinate algebra of the n × n quantum matrices is appropriate for the study the multiplicative property. It is shown that this basis is invariant under multiplication by certain quantum minors including the quantum determinant. Then a bas...