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Borel–de Siebenthal theory for affine reflection systems
Deniz Kusa, R. Venkateshb a University of Bochum, Faculty of Mathematics, Universitätsstr. 150, 44801 Bochum, Germany
b Department of Mathematics, Indian Institute of Science, Bangalore 560012
Abstract:
We develop a Borel–de Siebenthal theory for affine reflection systems by describing their maximal closed subroot systems. Affine reflection systems (introduced by Loos and Neher) provide a unifying framework for root systems of finite-dimensional semi-simple Lie algebras, affine and toroidal Lie algebras, and extended affine Lie algebras. In the special case of nullity $k$ toroidal Lie algebras, we obtain a one-to-one correspondence between maximal closed subroot systems with full gradient and triples $(q,(b_i),H)$, where $q$ is a prime number, $(b_i)$ is a $n$-tuple of integers in the interval $[0,q-1]$ and $H$ is a $(k\times k)$ Hermite normal form matrix with determinant $q$. This generalizes the $k=1$ result of Dyer and Lehrer in the setting of affine Lie algebras.
Key words and phrases:
extended affine Lie algebras, affine reflection systems, regular subalgebras.
Citation:
Deniz Kus, R. Venkatesh, “Borel–de Siebenthal theory for affine reflection systems”, Mosc. Math. J., 21:1 (2021), 99–127
Linking options:
https://www.mathnet.ru/eng/mmj788 https://www.mathnet.ru/eng/mmj/v21/i1/p99
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Abstract page: | 58 | References: | 14 |
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