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Cambridge University Press, Cambridge , p. Jon Jon 1 1 silver badge 5 5 bronze badges. Ringel The development of the representation theory of finite dimensional algebras. We study description of anyons in terms of matrix product operator algebras due to Bultinck et al. Marsh, I.
The articles cover various aspects of representations of Kac-Moody Lie algebras and their applications, structure of Leibniz algebras and Krichever-Novikov algebras, and related topics. The articles cover various aspects of representations of Kac-Moody Lie algebras and their applications, structure of Leibniz algebras and Krichever-Novikov algebras, representations of quantum groups, and related topics.
Bakalov and M. Sullivan, Inhomogeneous supersymmetric bilinear forms B. Cox, V. Futorny, and K.
Buy Kac-Moody Lie Algebras and Related Topics on compcommanalporth.gq ✓ FREE SHIPPING on qualified orders. Kac-Moody Lie Algebras and Related Topics cover image. Contemporary Mathematics Volume: ; ; pp; Softcover MSC: Primary
Cox and M. Im, On the module structure of the center of hyperelliptic Krichever-Novikov algebras I. Demir, Classification of 5-dimensional complex nilpotent Leibniz algebras V. Futorny, D.
Grantcharov, and L. Hong, Fusion rings revisited N.
I know very little Lie theory just the basics really, like in Kac's book and am not at all up to date on the current literature. I do know that in principle one could use KL polynomials to calculate characters, but that's not the kind of answer I'd like. Rather, I'd be interested in closed formulas like the Weyl-Kac character formula or explicit combinatorial descriptions of the weight space decomposition with respect to a Cartan. I'm sure no general results are known; I'll be happy with formulas for particular examples or special classes.
Other than that current techniques don't provide them. As one special case you may consider the Kac-Wakimoto admissible representations for affine Kac-Moody algebras. These representations are a bit more general than the integrable ones and satisfy modular invariance properties. Sign up to join this community. The best answers are voted up and rise to the top.
Home Questions Tags Users Unanswered. Character formulas for non-integrable modules? Ask Question. Asked 8 years, 9 months ago. Active 8 years, 8 months ago.
Viewed times. Sheikraisinrollbank Sheikraisinrollbank 1, 8 8 silver badges 7 7 bronze badges. But here no closed character formula like Weyl's can be expected in general, given the lack of Weyl group symmetry and complexity of KL polynomial values. For Kac-Moody algebras in general there is also lots of theory, but it gets even more complicated.
Many people have worked on this, such as Kashiwara, Tanisaki, Kumar,