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of 863
pro vyhledávání: '"Sherman , Alexander"'
We introduce Sylow subgroups and $0$-groups to the theory of complex algebraic supergroups, which mimic Sylow subgroups and $p$-groups in the theory of finite groups. We prove that Sylow subgroups are always $0$-groups, and show that they are unique
Externí odkaz:
http://arxiv.org/abs/2404.11077
The Cartan-Helgason theorem for supersymmetric spaces: spherical weights for Kac-Moody superalgebras
Autor:
Sherman, Alexander
Let $(\mathfrak{g},\mathfrak{k})$ be a supersymmetric pair arising from a finite-dimensional, symmetrizable Kac-Moody superalgebra $\mathfrak{g}$. An important branching problem is to determine the finite-dimensional highest-weight $\mathfrak{g}$-mod
Externí odkaz:
http://arxiv.org/abs/2403.19145
Autor:
Sherman, Alexander, Silberberg, Lior
We introduce a new, Kac-Moody-flavoured construction for Lie superalgebras, which seeks to incorporate phenomena of the queer Lie superalgebra. The idea of the generalization is to replace the maximal torus by a maximal quasitoral subalgebra, which h
Externí odkaz:
http://arxiv.org/abs/2309.09559
The maser, a microwave (MW) analog of the laser, is a well-established method for generating and amplifying coherent MW irradiation with ultra-low noise. This is accomplished by creating a state of population inversion between two energy levels separ
Externí odkaz:
http://arxiv.org/abs/2307.12691
We study the representation theory of the Lie superalgebra $\mathfrak{gl}(1|1)$, constructing two spectral sequences which eventually annihilate precisely the superdimension zero indecomposable modules in the finite-dimensional category. The pages of
Externí odkaz:
http://arxiv.org/abs/2307.06156
Autor:
Serganova, Vera, Sherman, Alexander
We present a general theorem which computes the cohomology of a homological vector field on global sections of vector bundles over smooth affine supervarieties. The hypotheses and results have the clear flavor of a localization theorem.
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Externí odkaz:
http://arxiv.org/abs/2210.13264
Autor:
Sherman, Alexander
We study ghost distributions on supersymmetric spaces for the case of basic classical Lie superalgebras. We introduce the notion of interlaced pairs, which are those for which both $(\mathfrak{g},\mathfrak{k})$ and $(\mathfrak{g},\mathfrak{k}')$ admi
Externí odkaz:
http://arxiv.org/abs/2208.09866
Given a Lie superalgebra $\mathfrak{g}$ and a maximal quasitoral subalgebra $\mathfrak{h}$, we consider properties of restrictions of $\mathfrak{g}$-modules to $\mathfrak{h}$. This is a natural generalization of the study of characters in the case wh
Externí odkaz:
http://arxiv.org/abs/2206.07709
Autor:
Serganova, Vera, Sherman, Alexander
We introduce the notion of splitting subgroups of quasireducitve supergroups, and explain their significance. For $GL(m|n)$, $Q(n)$, and defect one basic classical supergroups, we give explicit splitting subgroups. We further prove they are minimal u
Externí odkaz:
http://arxiv.org/abs/2206.07693
Autor:
Gorelik, Maria, Sherman, Alexander
We study the Duflo-Serganova functor $\operatorname{DS}_x$ for the queer Lie superalgebra $\mathfrak{q}_n$ and for all odd $x$ with $[x,x]$ semisimple. For the case when the rank of $x$ is $1$ we give a formula for multiplicities in terms of the arc
Externí odkaz:
http://arxiv.org/abs/2204.05048