منابع مشابه
8 Piecewise Linear Parametrization of Canonical Bases
In [L1] the author introduced the canonical basis for the plus part of a quantized enveloping algebra of type A,D or E. (The same method applies for nonsimplylaced types, see [L3, 12.1].) Another approach to the canonical basis was later found in [Ka]. In [L1] we have also found that the set parametrizing the canonical basis has a natural piecewise linear structure that is, a collection of bije...
متن کاملCanonical Bases and Piecewise-linear Combinatorics
Let Uq be the quantum group associated to a Lie algebra g of rank n. The negative part U q of Uq has a canonical basis B with favourable properties (see Kashiwara [3] and Lusztig [6, §14.4.6]). The approaches of Lusztig and Kashiwara lead to a set of alternative parametrizations of the canonical basis, one for each reduced expression for the longest word in the Weyl group of g. We describe the ...
متن کاملCanonical Proofs for Linear Logic Programming Frameworks
We discuss here the proof-theoretic foundations for theorem proving and logic programming in linear logic, mainly studying how to deene canonical proofs (that are complete) for eecient proof search in fragments of linear logic. We analyze the conception of such proof forms, for frameworks based on proof-construction as computation, emphasizing the relationship between the logical fragment and i...
متن کاملDual Canonical Bases for the Quantum General Linear Supergroup
Dual canonical bases of the quantum general linear supergroup are constructed which are invariant under the multiplication of the quantum Berezinian. By setting the quantum Berezinian to identity, we obtain dual canonical bases of the quantum special linear supergroup Oq(SLm|n). We apply the canonical bases to study invariant subalgebras of the quantum supergroups under left and right translati...
متن کاملOn 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...
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ژورنال
عنوان ژورنال: Linear Algebra and its Applications
سال: 1988
ISSN: 0024-3795
DOI: 10.1016/0024-3795(88)90322-9