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Representations of Complex Semi-Simple Lie Groups and Lie Algebras [PDF]
The Annals of Mathematics, 1966 Let \(\mathfrak g\) be a complex semisimple Lie algebra, \(\mathfrak h\) a Cartan subalgebra of \(\mathfrak g\) and \(\Delta\) the set of roots of \(\mathfrak g\) with respect to \(\mathfrak h\). For any positive system \(P\) of roots we denote by \(D_P\) the set of all \(\lambda\in\mathfrak h^*\) which are integral and dominant relative to \(P\). Let \
Parthasarathy, K. R. +2 more
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On a Sufficient Condition for the Existence of a Periodic Part in the Shunkov Group
Известия Иркутского государственного университета: Серия "Математика", 2017 The group $ G $ is saturated with groups from the set of groups if any a finite subgroup $ K $ of $ G $ is contained in a subgroup of $ G $, which is isomorphic to some group in $ \mathfrak{X} $.
A.A. Shlepkin
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Varieties of a class of elementary subalgebras
AIMS Mathematics, 2022 Let $ G $ be a connected standard simple algebraic group of type $ C $ or $ D $ over an algebraically closed field $ \Bbbk $ of positive characteristic $ p > 0 $, and $ \mathfrak{g}: = \mathrm{Lie}(G) $ be the Lie algebra of $ G $.
Yang Pan, Yanyong Hong
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Langlands duality for representations of quantum groups [PDF]
, 2010 We establish a correspondence (or duality) between the characters and the crystal bases of finite-dimensional representations of quantum groups associated to Langlands dual semi-simple Lie algebras. This duality may also be stated purely in terms of semi-
D. Hernandez +17 more
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THE SHMUSHKEVICH METHOD FOR HIGHER SYMMETRY GROUPS OF INTERACTING PARTICLES
Acta Polytechnica, 2013 About 60 years ago, I. Shmushkevich presented a simple ingenious method for computing the relative probabilities of channels involving the same interacting multiplets of particles, without the need to compute the Clebsch-Gordan coefficients.
Mark Bodner +3 more
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Gauging Lie group symmetry in (2+1)d topological phases
SciPost Physics, 2023 We present a general algebraic framework for gauging a 0-form compact, connected Lie group symmetry in (2+1)d topological phases. Starting from a symmetry fractionalization pattern of the Lie group $G$, we first extend $G$ to a larger symmetry group ...
Meng Cheng, Po-Shen Hsin, Chao-Ming Jian
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A product theorem in simple Lie groups [PDF]
Geometric and Functional Analysis, 2015 We prove a discretized Product Theorem for general simple Lie groups, in the spirit of Bourgain's Discretized Sum-Product Theorem.
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A modular analogue of Morozov's theorem on maximal subalgebras of simple Lie algebras [PDF]
, 2017 Let $G$ be a simple algebraic group over an algebraically closed field of characteristic $p>0$ and suppose that $p$ is a very good prime for $G$. We prove that any maximal Lie subalgebra $M$ of $\mathfrak{g} = {\rm Lie}(G)$ with ${\rm rad}(M) \ne 0$ has ...
Benkart +52 more
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ON CUBATURE RULES ASSOCIATED TO WEYL GROUP ORBIT FUNCTIONS
Acta Polytechnica, 2016 The aim of this article is to describe several cubature formulas related to the Weyl group orbit functions, i.e. to the special cases of the Jacobi polynomials associated to root systems.
Lenka Háková +2 more
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Hurwitz components of groups with socle PSL(3, q)
Extracta Mathematicae, 2021 For a finite group G, the Hurwitz space Hinr,g(G) is the space of genus g covers of the Riemann sphere P1 with r branch points and the monodromy group G. In this paper, we give a complete list of some almost simple groups of Lie rank two.
H.M. Mohammed Salih
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