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This article is cited in 9 scientific papers (total in 9 papers)
Second order Casimirs for the affine Krichever–Novikov algebras $\widehat{\mathfrak{gl}}_{g,2}$ and $\widehat{\mathfrak{sl}}_{g,2}$
O. K. Sheinmanab a Steklov Mathematical Institute, Russian Academy of Sciences
b Independent University of Moscow
Abstract:
The second order casimirs for the affine Krichever–Novikov algebras $\widehat{\mathfrak{gl}}_{g,2}$ and $\widehat{\mathfrak{sl}}_{g,2}$ are described. More general operators which we call semi-casimirs are introduced. It is proven that the semi-casimirs induce well-defined operators on conformal blocks and, for a certain moduli space of Riemann surfaces with two marked points and fixed jets of local coordinates, there is a natural projection of its tangent space onto the space of these operators.
Key words and phrases:
Infinite-dimensional Lie algebras, Riemann surfaces, current algebras, central extensions, highest weight representations, wedge representations, Casimir operators, moduli spaces, conformal blocks.
Citation:
O. K. Sheinman, “Second order Casimirs for the affine Krichever–Novikov algebras $\widehat{\mathfrak{gl}}_{g,2}$ and $\widehat{\mathfrak{sl}}_{g,2}$”, Mosc. Math. J., 1:4 (2001), 605–628
Linking options:
https://www.mathnet.ru/eng/mmj40 https://www.mathnet.ru/eng/mmj/v1/i4/p605
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Abstract page: | 264 | Full-text PDF : | 2 | References: | 57 |
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