Yuan Yao,University of Toronto, Department of Mathematics, 40 St George Street, Toronto, Ontario, Canada M4S 2E4; e-mail: yy.yao@mail.utoronto.ca

Abstract/Résumé:

For root systems of symmetrizable Kac-Moody algebras, we study a tiling of the positive root cone of the form \(\bigcup_{w\in W} (1-w) C ^+\), where \(W\) is the Weyl group and \(C^+\) is the fundamental chamber. We show for general symmetrizable Kac-Moody algebras the tiles are disjoint, and the gaps between top dimensional tiles have codimension \(\geq2\). For affine Kac-Moody algebras we completely describe the closure \(\bigcup_{w\in W} \overline{(1-w) C ^+}\).

Pour les systèmes des racines d’algèbres de Kac-Moody symétriques, nous étudions un carrelage du cône des racines positifs de la forme \(\bigcup_{w\in W} (1-w) C ^+\), où \(W\) est le groupe de Weyl et \( C^+ \) est la chambre fondamentale. Nous montrons que les carreaux sont disjoints pour les algèbres de Kac-Moody symétriques, et les lacunes entre les carreaux de dimension supérieure ont codimension \(\geq 2\). Pour les algèbres de Kac-Moody affines, nous décrivons complètement \(\bigcup_{w\in W} \overline{(1-w) C ^+}\).

Keywords: Kac-Moody Algebras, Root System, Tiling

AMS Subject Classification: , Kac-Moody (super)algebras (structure and representation theory) 17B22, 17B67

PDF(click to download): Tilings Defined by Root Systems of Kac-Moody Algebras

Y. Gao / N. Jing

Abstract/Résumé:

No abstract available but the full text pdf may be downloaded at the title link below.

Keywords:

AMS Subject Classification: Quantum groups (quantized enveloping algebras) and related deformations, Kac-Moody (super)algebras (structure and representation theory), Vertex operators; vertex operator algebras and related structures 17B37, 17B67, 17B69

PDF(click to download): Algebras over the Fock space

A. Grishkov

Abstract/Résumé:

No abstract available but the full text pdf may be downloaded at the title link below.

Keywords:

AMS Subject Classification: Structure theory, Simple; semisimple; reductive (super)algebras (roots), Kac-Moody (super)algebras (structure and representation theory) 17B05, 17B20, 17B67

PDF(click to download): Representations of completely solvable Lie algebras over a ring of polynomials

V.M. Futorny / A.N. Grishkov / D.J. Melville

Abstract/Résumé:

No abstract available but the full text pdf may be downloaded at the title link below.

Keywords:

AMS Subject Classification: Quantum groups (quantized enveloping algebras) and related deformations, Kac-Moody (super)algebras (structure and representation theory), Quantum groups and related algebraic methods 17B37, 17B67, 81R50

PDF(click to download): Quantum imaginary Verma modules for affine Lie algebras