Introduces and classifies objects in a Whittaker category for W(n), then establishes a Skryabin-type equivalence for its finite W-superalgebra.
Whittaker Modules for W type Cartan Lie superalgebras
2 Pith papers cite this work. Polarity classification is still indexing.
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Pith papers citing it
abstract
We consider the category of Whittaker modules for the Lie superalgebra $W_{m,n}$ of vector fields on $\mathbb{C}^{(m|n)}$. For any $\mathbf{a}\in \mathbb{C}^m$ we show the equivalence between the blocks $\Omega_{\mathbf a}^{\widetilde{W}_{m,n}}$ of the category of $(AW)_{m,n}$-Whittaker modules with finite-dimensional Whittaker vector spaces and the category of finite-dimensional modules over certain Lie subsuperalgebra $T_{m,n}$ of $(AW)_{m,n}$ (and also of $\mathfrak{gl}{(m,n)})$. Then we apply the covering technique to study Whittaker $W_{m,n}$-modules and describe simple modules in the category $\Omega_{\mathbf a}^{{W}_{m,n}}$ of such modules with finite-dimensional Whittaker vector spaces and with non-singular ${\mathbf a}$.
fields
math.RT 2years
2026 2verdicts
UNVERDICTED 2representative citing papers
Establishes irreducibility of imaginary Whittaker modules over affine and quantum affine algebras using parabolic induction, including new non-deformation examples.
citing papers explorer
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Whittaker Category and Finite W-superalgebras for Cartan Type Lie Superalgebras
Introduces and classifies objects in a Whittaker category for W(n), then establishes a Skryabin-type equivalence for its finite W-superalgebra.
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Whittaker constructions for quantum affine algebras
Establishes irreducibility of imaginary Whittaker modules over affine and quantum affine algebras using parabolic induction, including new non-deformation examples.