2024/04/29 by Marco Matassa, Matassa, Marco
Physics and Astronomy · Mathematics · #Nonlinear Waves and Solitons #Advanced Topics in Algebra #Numerical methods for differential equations
paper · pdf · doi:10.48550/arxiv.2404.18544
Consider a decomposition \mathfrakn = \mathfrakn1 ⊕ ⋯ ⊕ \mathfraknr of the positive nilradical of a complex semisimple Lie algebra of rank r, where each \mathfraknk is a module under an appropriate Levi factor. We show that this can be quantized as a finite-dimensional subspace \mathfraknqk = \mathfraknq1 ⊕ ⋯ ⊕ \mathfraknqr of the positive part of the quantized enveloping algebra, where each \mathfraknqk is a module under the left adjoint action of a quantized Levi factor. Furthermore, we show that ℂ ⊕ \mathfraknq is a left coideal, with the possible exception of components corresponding to some exceptional Lie algebras. Finally we use these quantizations to construct covariant first-order differential calculi on quantum flag manifolds, compatible in a certain sense with the decomposition above, which coincide with those introduced by Heckenberger-Kolb in the irreducible case.