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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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This content will become publicly available on October 29, 2025
Invariant theory for the commuting scheme of symplectic Lie algebras
We prove the Chevalley restriction theorem for the commuting scheme of symplectic Lie algebras. The key step is the construction of the inverse map of the Chevalley restriction map called the spectral data map. Along the way, we establish a certain multiplicative property of the Pfaffian which is of independent interest.
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- Award ID(s):
- 2001257
- PAR ID:
- 10552685
- Publisher / Repository:
- Tata Institute of Fundamental Research Publications
- Date Published:
- ISSN:
- ####-####
- ISBN:
- 978-81-957829-7-0
- Format(s):
- Medium: X
- Location:
- Tata Institute of Fundamental Research
- Sponsoring Org:
- National Science Foundation
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