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Cohomology and Crossed Module Extensions of Hom-Leibniz–Rinehart Algebras
In this paper, we introduce the concept of crossed module for Hom-Leibniz–Rinehart algebras. We then study the cohomology and extension theory of...
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Weight Modules
The theory of weight modules over reductive Lie algebras is a well-established branch of representation theory. For root-reductive Lie algebras, the...
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Classification of simple bounded weight modules of the Lie algebra of vector fields on ℂn
Let W
n + be the Lie algebra of vector fields on ℂ n . In this paper, we classify all simple bounded weight modules. Any such module is isomorphic to... -
Weak Faces of Highest Weight Modules and Root Systems
Chari and Greenstein (Adv. Math. 220 (4), 1193–1221,
2009 ) introduced certain combinatorial subsets of the roots of a finite-dimensional simple Lie... -
Bounded Weight Modules Over the Lie Superalgebra of Cartan W-type
Let A m , n be the tensor product of the polynomial algebra in m even variables and the exterior algebra in n odd variables over the complex field
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A classification of harmonic weak Maaß forms of half-integral weight
We classify Harish-Chandra modules generated by the pullback to the metaplectic group of harmonic weak Maaß forms with exponential growth allowed at...
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On Minimal Tilting Complexes in Highest Weight Categories
We explain the construction of minimal tilting complexes for objects of highest weight categories and we study in detail the minimal tilting...
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Bilinear forms in the Jacobian module and binding of N-spectral chains of a hypersurface with an isolated singularity
Using his deep and beautiful idea of cutting with a Hyperplane, Lefschetz explained how the homology groups of a projective smooth variety could be...
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Radon–Kipriyanov Transform of Laplace Series by Weight Spherical Functions
AbstractIn this paper we consider the Radon–Kipriyanov transform and its relationship with the special Radon transform. The representation of plane...
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Lie Algebroids and Weight Systems
We put the Rozansky-Witten weight systems obtained from Lie algebroids by Voglaire & Xu, into the general machine provided by Kontsevich in the...
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The Module-Phase Synchronization of Complex-Valued Neural Networks with Time-Varying Delay and Stochastic Perturbations
The problem of exponential module-phase synchronization of complex-valued neural networks (CVNNs) with time-varying delay and stochastic...
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Weight Systems of Framed Chord Diagrams Corresponding to Lie Algebras
AbstractThe Bar-Natan construction of weight systems induced by Lie algebra representations is generalized in the paper to the case of framed chord...
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Transfer of Highest Weight Modules and Small Unipotent Representations
We study the transfer between small special unipotent representations for all equal rank real forms of type E 6 and E 7 . As a consequence, one can...
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Affine RSK Correspondence and Crystals of Level Zero Extremal Weight Modules
We give an affine analogue of the Robinson-Schensted-Knuth (RSK) correspondence, which generalizes the affine Robinson-Schensted correspondence by...
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Equivariant K-theory of the semi-infinite flag manifold as a nil-DAHA module
The equivariant K -theory of the semi-infinite flag manifold, as developed recently by Kato, Naito, and Sagaki, carries commuting actions of the...
