Shapovalov determinant for loop superalgebras
2008 (English)In: Theoretical and mathematical physics, ISSN 0040-5779, E-ISSN 1573-9333, Vol. 156, no 3, 1292-1307 p.Article in journal (Refereed) Published
For the Kac-Moody superalgebra associated with the loop superalgebra with values in a finite-dimensional Lie superalgebra g, we show what its quadratic Casimir element is equal to if the Casimir element for g is known (if g has an even invariant supersymmetric bilinear form). The main tool is the Wick normal form of the even quadratic Casimir operator for the Kac-Moody superalgebra associated with g; this Wick normal form is independently interesting. If g has an odd invariant supersymmetric bilinear form, then we compute the cubic Casimir element. In addition to the simple Lie superalgebras g = g(A) with a Cartan matrix A for which the Shapovalov determinant was known, we consider the Poisson Lie superalgebra poi(0 vertical bar n) and the related Kac-Moody superalgebra.
Place, publisher, year, edition, pages
2008. Vol. 156, no 3, 1292-1307 p.
Lie superalgebra, Shapovalov determinant
Physical Sciences Mathematics
IdentifiersURN: urn:nbn:se:su:diva-57861DOI: 10.1007/s11232-008-0107-7ISI: 000259821400005OAI: oai:DiVA.org:su-57861DiVA: diva2:418368
authorCount :22011-05-232011-05-232011-05-23Bibliographically approved