For a given weight of a complex simple Lie algebra, the q-analog of
Kostant’s partition function is a polynomial valued function in the variable q, where the coefficient of qk is the number of ways the weight can be
written as a nonnegative integral sum of exactly k positive roots. In this
paper we determine generating functions for the q-analog of Kostant’s
partition function when the weight in question is the highest root of the
classical Lie algebras of types B, C, and D, and the exceptional Lie
algebras of type G2, F4, E6, E7, and E8.
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This content will become publicly available on January 1, 2026
Semisimplification of contragredient Lie algebras
We describe the structure and different features of Lie algebras in the Verlinde category, obtained as semisimplification of contragredient Lie algebras in characteristic p with respect to the adjoint action of a Chevalley generator. In particular, we construct a root system for these algebras that arises as a parabolic restriction of the known root system for the classical Lie algebra. This gives a lattice grading with simple homogeneous components and a triangular decomposition for the semisimplified Lie algebra. We also obtain a non-degenerate invariant form that behaves well with the lattice grading. As an application, we exhibit concrete new examples of Lie algebras in the Verlinde category.
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- Award ID(s):
- 2146392
- PAR ID:
- 10518486
- Publisher / Repository:
- MSP (Mathematical Sciences Publishers).
- Date Published:
- Journal Name:
- Orbita Mathematicae
- Volume:
- 2
- Issue:
- 1
- ISSN:
- 2993-6144
- Page Range / eLocation ID:
- 1 to 32
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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