An LLT-type algorithm for computing higher-level canonical bases
نویسنده
چکیده
We give a fast algorithm for computing the canonical basis of an irreducible highest-weight module for Uq(ŝle), generalising the LLT algorithm.
منابع مشابه
A new algorithm for computing SAGBI bases up to an arbitrary degree
We present a new algorithm for computing a SAGBI basis up to an arbitrary degree for a subalgebra generated by a set of homogeneous polynomials. Our idea is based on linear algebra methods which cause a low level of complexity and computational cost. We then use it to solve the membership problem in subalgebras.
متن کاملConstructing Canonical Bases of Quantized Enveloping Algebras
Since the invention of canonical bases of quantized enveloping algebras, one of the main problems has been to establish what they look like. Explicit formulas are only known in a few cases corresponding to root systems of low rank, namely A1 (trivial), A2 ([Lusztig 90]), A3 ([Xi 99a]), and B2 ([Xi 99b]). Furthermore, there is evidence suggesting that for higher ranks the formulas become so comp...
متن کاملApplying Buchberger's criteria on Montes's DisPGB algorithm
The concept of comprehensive Grobner bases was introduced by Weispfenning. Montes has proposed an efficient algorithm for computing these bases. But he has not explicitly used Buchberger's criteria in his algorithm. In this paper we prove that we can apply these criteria on Montes algorithm. We propose a modified version of Montes algorithm and evaluate its performance via some examples.
متن کاملQuiver Schur Algebras for the Linear Quiver I
We define a graded quasi-hereditary covering for the cyclotomic quiver Hecke algebras Rn of type A when e = 0 (the linear quiver) or e ≥ n. We show that these algebras are quasi-hereditary graded cellular algebras by giving explicit homogeneous bases for them. When e = 0 we show that the KLR grading on the quiver Hecke algebras is compatible with the gradings on parabolic category OΛ n previous...
متن کاملCanonical bases of higher-level q-deformed Fock spaces and Kazhdan-Lusztig polynomials
The aim of this paper is to generalize several aspects of the recent work of LeclercThibon and Varagnolo-Vasserot on the canonical bases of the level 1 q-deformed Fock spaces due to Hayashi. Namely, we define canonical bases for the higher-level qdeformed Fock spaces of Jimbo-Misra-Miwa-Okado and establish a relation between these bases and (parabolic) Kazhdan-Lusztig polynomials for the affine...
متن کامل