FULL HEAPS AND REPRESENTATIONS OF AFFINE KAC-MOODY ALGEBRAS

R. M. Green

Makale detayları

FULL HEAPS AND REPRESENTATIONS OF AFFINE KAC-MOODY ALGEBRAS

Yazarlar:

R. M. Green

Yayıncı:

Abdullah HARMANCI

Dergi:

International Electronic Journal of Algebra 2007 Vol.2 Issue 2, pp.137-188

Belge Tipi:

Makale

Yayın Tarihi:

11/2007

Belge Dili:

Türkçe

Document ID (Org No.):

2000718448

Sıklık:

Aylık

eISSN:

1306-6048

pISSN:

1306-6048

Özet:

 

We give a combinatorial construction, not involving a presentation, of almost all untwisted affine Kac-Moody algebras modulo their onedimensional centres in terms of signed raising and lowering operators on a certain distributive lattice B. The lattice B is constructed combinatorially as a set of ideals of a “full heap” over the Dynkin diagram, which leads to a kind of categorification of the positive roots for the Kac-Moody algebra. The lattice B is also a crystal in the sense of Kashiwara, and its span affords representations of the associated quantum affine algebra and affine Weyl group. There are analogues of these results for two infinite families of twisted affine Kac-Moody algebras, which we hope to treat more fully elsewhere. By restriction, we obtain combinatorial constructions of the finite dimensional simple Lie algebras over C, except those of types E8, F4 and G2. The Chevalley basis corresponding to an arbitrary orientation of the Dynkin diagram is then represented explicitly by raising and lowering operators. We also obtain combinatorial constructions of the spin modules for Lie algebras of types B and D, which avoid Clifford algebras, and in which the action of Chevalley bases on the canonical bases of the modules may be explicitly calculated.

Makale detayları

FULL HEAPS AND REPRESENTATIONS OF AFFINE KAC-MOODY ALGEBRAS

Yazarlar: R. M. Green

Yayıncı: Abdullah HARMANCI

Dergi: International Electronic Journal of Algebra 2007 Vol.2 Issue 2, pp.137-188

Belge Tipi: Makale

Yayın Tarihi: 11/2007

Belge Dili: Türkçe

Document ID (Org No.): 2000718448

Sıklık: Aylık

eISSN: 1306-6048

pISSN: 1306-6048

Sayı

Yazarlar:

R. M. Green

Yayıncı:

Abdullah HARMANCI

Dergi:

International Electronic Journal of Algebra 2007 Vol.2 Issue 2, pp.137-188

Belge Tipi:

Makale

Yayın Tarihi:

11/2007

Belge Dili:

Türkçe

Document ID (Org No.):

2000718448

Sıklık:

Aylık

eISSN:

1306-6048

pISSN:

1306-6048