Link Invariants and Lie Superalgebras

DOI

10.2991/jnmp.2005.12.s1.30How to use a DOI?

Abstract

Berger and Stassen reviewed skein relations for link invariants coming from the simple Lie algebras g. They related the invariants with decomposition of the tensor square of the g-module V of minimal dimension into irreducible components. (If V V , one should also consider the decompositions of V V and V V .) Here we consider decompositions into irreducible components for g-modules V of minimal dimension over some simple and close to simple Lie superalgebras g. For the classical series (gl, sl, osp), as well as for the Poisson and Hamiltonian algebras -- "quasi-classical" analogs of gl and sl -- the answer is rather complicated due to the lack of complete reduciblity. Contrariwise, the case of exceptional Lie superalgebras g = ag2 and ab3 turned out to be similar to that of Lie algebras: The g-module g g (here the representation of minimal dimension is the adjoint one) is completely reducible and, remarkably, the spectra of highest weights for ag2 are almost identical (in certain coordinates) to that for ab3! We also consider g = osp(4|2) for = 0, 1.

Copyright

© 2006, the Authors. Published by Atlantis Press.

Open Access

This is an open access article distributed under the CC BY-NC license (http://creativecommons.org/licenses/by-nc/4.0/).

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TY  - JOUR
AU  - P. Grozman
AU  - D. Leites
PY  - 2005
DA  - 2005/01/01
TI  - Link Invariants and Lie Superalgebras
JO  - Journal of Nonlinear Mathematical Physics
SP  - 372
EP  - 379
VL  - 12
IS  - Supplement 1
SN  - 1776-0852
UR  - https://doi.org/10.2991/jnmp.2005.12.s1.30
DO  - 10.2991/jnmp.2005.12.s1.30
ID  - Grozman2005
ER  -