Universität zu Köln

Backhaus, Teodor, Fang, Xin and Fourier, Ghislain (2017). DEGREE CONES AND MONOMIAL BASES OF LIE ALGEBRAS AND QUANTUM GROUPS. Glasg. Math. J., 59 (3). S. 595 - 622. NEW YORK: CAMBRIDGE UNIV PRESS. ISSN 1469-509X

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Abstract

We provide N-filtrations on the negative part U-q(n(-)) of the quantum group associated to a finite-dimensional simple Lie algebra g, such that the associated graded algebra is a skew-polynomial algebra on n(-). The filtration is obtained by assigning degrees to Lusztig's quantum PBW root vectors. The possible degrees can be described as lattice points in certain polyhedral cones. In the classical limit, such a degree induces an N-filtration on any finite-dimensional simple g-module. We prove for type A(n), C-n, B-3, D-4 and G(2) that a degree can be chosen such that the associated graded modules are defined by monomial ideals, and conjecture that this is true for any g.

Item Type:	Journal Article
Creators:	Creators Email ORCID ORCID Put Code Backhaus, Teodor UNSPECIFIED UNSPECIFIED UNSPECIFIED Fang, Xin UNSPECIFIED UNSPECIFIED UNSPECIFIED Fourier, Ghislain UNSPECIFIED UNSPECIFIED UNSPECIFIED
URN:	urn:nbn:de:hbz:38-219760
DOI:	10.1017/S0017089516000422
Journal or Publication Title:	Glasg. Math. J.
Volume:	59
Number:	3
Page Range:	S. 595 - 622
Date:	2017
Publisher:	CAMBRIDGE UNIV PRESS
Place of Publication:	NEW YORK
ISSN:	1469-509X
Language:	English
Faculty:	Faculty of Mathematics and Natural Sciences
Divisions:	Faculty of Mathematics and Natural Sciences > Department of Mathematics and Computer Science > Mathematical Institute
Subjects:	no entry
Uncontrolled Keywords:	Keywords Language CANONICAL BASES; PBW FILTRATION; POLYTOPES; MODULES; A(N) Multiple languages Mathematics Multiple languages
Refereed:	Yes
URI:	http://kups.ub.uni-koeln.de/id/eprint/21976