منابع مشابه
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...
متن کاملDecomposition numbers and canonical bases
We obtain some simple relations between decomposition numbers of quantized Schur algebras at an nth root of unity (over a field of characteristic 0). These relations imply that every decomposition number for such an algebra occurs as a decomposition number for some Hecke algebra of type A. We prove similar relations between coefficients of the canonical basis of the q-deformed Fock space repres...
متن کاملCanonical Bases of Borcherds - Cartan
We study the canonical basis for the negative part U− of the quantum generalized Kac-Moody algebra associated to a symmetric BorcherdsCartan matrix. The algebras U− associated to two different matrices satisfying certain conditions may coincide (6.3). We show that the canonical bases coincide provided that the algebras U− coincide (Theorem 6.3.5). We also answer partially a question by Lusztig ...
متن کاملDecorated Tangles and Canonical Bases
We study the combinatorics of fully commutative elements in Coxeter groups of type H n for any n > 2. Using the results, we construct certain canonical bases for non-simply-laced generalized Temperley{Lieb algebras and show how to relate them to morphisms in the category of decorated tangles.
متن کاملCanonical Bases for Algebraic Computations
We investigate, for quotients of the non-commutative polynomial ring, a property that implies finiteness of Gröbner bases computation, and examine its connection with Noetherianity. We propose a Gröbner bases theory for our factor algebras, of particular interest for one-sided ideals, and show a few applications, e.g. how to compute (one-sided) syzygy modules.
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ژورنال
عنوان ژورنال: Advances in Mathematics
سال: 2017
ISSN: 0001-8708
DOI: 10.1016/j.aim.2017.06.005