POSITIVITY AND THE CANONICAL BASIS OF TENSOR PRODUCTS OF FINITE-DIMENSIONAL IRREDUCIBLE REPRESENTATIONS OF QUANTUM sl(k)
نویسنده
چکیده
In a categorification of tensor products of fundamental representations of quantum sl(k) via highest weight categories, the indecomposable tilting modules descend to the canonical basis. Projective functors map tilting modules to tilting modules implying the coefficients of the canonical basis of tensor products of finite dimensional, irreducible representations under the action of the Chevalley generators are positive.
منابع مشابه
The Hall algebra of a cyclic quiver and canonical bases of Fock spaces
where x ∈ Ŝk is minimal such that ν = λ.x satisfies νi < νi+1 for i = 1, 2 . . . k− 1 and νi− νk ≥ 1− k−n, and μ = λ.x y. This conjecture is proved by Kazhdan-Lusztig [KL] and Kashiwara-Tanisaki [KT]. The proof relies on an equivalence between the category of finite-dimensional Uǫ(slk)-modules and a category of negative-level representations of the affine algebra ŝlk which are integrable with r...
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