✦ LIBER ✦

The Lusztig Cones of a Quantized Enveloping Algebra of Type A

✍ Scribed by Robert Marsh

Publisher: Elsevier Science
Year: 2001
Tongue: English
Weight: 135 KB
Volume: 244
Category: Article
ISSN: 0021-8693
DOI: 10.1006/jabr.2001.8924

No coin nor oath required. For personal study only.

✦ Synopsis

We show that for each reduced expression for the longest word in the Weyl group of type A , the corresponding cone arising in Lusztig's description of the n canonical basis in terms of tight monomials is simplicial, and construct explicit spanning vectors.

📜 SIMILAR VOLUMES

Rectangle Diagrams for the Lusztig Cones

Rectangle Diagrams for the Lusztig Cones of Quantized Enveloping Algebras of Type A

✍ Robert Marsh 📂 Article 📅 2002 🏛 Elsevier Science 🌐 English ⚖ 239 KB

Let U be the quantum group associated to a Lie algebra g of type A n . The negative part U -of U has a canonical basis B defined by Lusztig and Kashiwara, with favorable properties. We show how the spanning vectors of the cones defined by Lusztig (1993, Israel Math. Conf. Proc. 7, 117-132), when reg

Regions of Linearity, Lusztig Cones, and

Regions of Linearity, Lusztig Cones, and Canonical Basis Elements for the Quantized Enveloping Algebra of Type A4

✍ Roger Carter; Robert Marsh 📂 Article 📅 2000 🏛 Elsevier Science 🌐 English ⚖ 421 KB

to professor helmut wielandt on his 90th birthday Let U q be the quantum group associated to a Lie algebra g of rank n. The negative part U -of U has a canonical basis B with favourable properties (see M. Kashiwara (1991, Duke Math. J. 63, 465-516) and G. Lusztig (1993. "Introduction to Quantum Grou

A Completion of the Quantized Enveloping

A Completion of the Quantized Enveloping Algebra of a Kac–Moody Algebra

✍ Anthony Joseph 📂 Article 📅 1999 🏛 Elsevier Science 🌐 English ⚖ 319 KB

On the Center of Quantized Enveloping Al

On the Center of Quantized Enveloping Algebras

✍ Pierre Baumann 📂 Article 📅 1998 🏛 Elsevier Science 🌐 English ⚖ 266 KB

Let U be a quasitriangular Hopf algebra. One may use the R-matrix of U in order to construct scalar invariants of knots. Analogously, Reshetikhin wrote down tangle invariants which take their values in the center of U. Reshetikhin's expressions thus define central elements in U. We prove here an ide

q-Wedge Modules for Quantized Enveloping

q-Wedge Modules for Quantized Enveloping Algebras of Classical Type

✍ Naihuan Jing; Kailash C. Misra; Masato Okado 📂 Article 📅 2000 🏛 Elsevier Science 🌐 English ⚖ 158 KB

We use the fusion construction in twisted quantum affine algebras to obtain a unified method to deform the wedge product for classical Lie algebras. As a by-product we uniformly realize all non-spin fundamental modules for quantized enveloping algebras of classical types, and show that they admit na

Special Bases of Irreducible Modules of

Special Bases of Irreducible Modules of the Quantized Universal Enveloping Algebra Uv(gl(n))

✍ N.H. Xi 📂 Article 📅 1993 🏛 Elsevier Science 🌐 English ⚖ 299 KB

In this paper we construct a basis for an irreducible module of the quantized enveloping algebra \(U_{r}(g /(n))\) which is a \(q\)-analogue of the special basis of an irreducible \(G L(n)\)-module introduced by C. de Concini and D. Kazhdan (Israel J. Math. 40, 1980, 275-290). We conjecture the basi