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On the Cohomology of Certain Rank 2 Vector Bundles on G/B
Let G be a semisimple, simply connected, linear algebraic group over an algebraically closed field k . Donkin (In J. Algebra, 307, 570–613
2007 ),... -
The Periplectic Brauer Algebra III: The Deligne Category
We construct a faithful categorical representation of an infinite Temperley-Lieb algebra on the periplectic analogue of Deligne’s universal monoidal...
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Generalized Oscillator Representations of the Twisted Heisenberg-Virasoro Algebra
In this paper, we first obtain a general result on sufficient conditions for tensor product modules to be simple over an arbitrary Lie algebra. We...
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k-Modules Over Linear Spaces by n-Linear Maps Admitting a Multiplicative Basis
We study the structure of certain k -modules 𝕍 over linear spaces 𝕎 with restrictions neither on the dimensions of 𝕍 and 𝕎 nor on the base field...
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Irreducible Wakimoto-like Modules for the Lie Superalgebra D(2, 1;α)
By using the idea of Wakimoto’s free field, we construct a class of representations for the Lie superalgebra D (2, 1; α) on the tensor product of a...
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On the centers of quantum groups of A n -type
Let g be the finite dimensional simple Lie algebra of type An, and let U̅ = U q (g,Λ) and U = U q (g, Q ) be the quantum groups defined over the weight...
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PBW Degeneration: Algebra, Geometry, and Combinatorics
We review the recent progress in the theory of Poincaré–Birkhoff–Witt degenerations of irreducible representations of simple Lie algebras. We...
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Equivalence of formulations of the MKP hierarchy and its polynomial tau-functions
We show that a system of Hirota bilinear equations introduced by Jimbo and Miwa defines tau-functions of the modified KP (MKP) hierarchy of evolution...