Canonical bases and higher representation theory
نویسندگان
چکیده
منابع مشابه
Representation theory of p-adic groups and canonical bases
In this paper, we interpret the Gindikin–Karpelevich formula and the Casselman–Shalika formula as sums over Kashiwara–Lusztig’s canonical bases, generalizing the results of Bump and Nakasuji (2010) [7] to arbitrary split reductive groups. We also rewrite formulas for spherical vectors and zonal spherical functions in terms of canonical bases. In a subsequent paper Kim and Lee (preprint) [14], w...
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We fix an algebraically closed field k of characteristic zero. Let G be a reductive affine algebraic group over k and let V be an affine G-variety over k. We denote by A(G) and A(V ) the k-algebras of regular functions on G and V respectively. The action of G on V gives rise to a rational representation of G on A(V ). A natural question is to investigate whether the algebra A(V ) is a free modu...
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We give a fast algorithm for computing the canonical basis of an irreducible highest-weight module for Uq(ŝle), generalising the LLT algorithm.
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We define canonical bases of the higher-level q-deformed Fock space modules of the affine Lie algebra sl n generalizing the result of Leclerc and Thibon for the case of level 1. We express the transition matrices between the canonical bases and the natural bases of the Fock spaces in terms of certain affine Kazhdan-Lusztig polynomials. Leclerc and Thibon defined, in [6], a canonical basis of th...
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We identify a new representation of propositional knowledge bases, the Sentential Decision Diagram (SDD), which is interesting for a number of reasons. First, it is canonical in the presence of additional properties that resemble reduction rules of OBDDs. Second, SDDs can be combined using any Boolean operator in polytime. Third, CNFs with n variables and treewidth w have canonical SDDs of size...
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ژورنال
عنوان ژورنال: Compositio Mathematica
سال: 2014
ISSN: 0010-437X,1570-5846
DOI: 10.1112/s0010437x1400760x