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The H-polynomial of an irreducible representation
Journal of Algebra, 2011 Associated with the finite-dimensional rational representation \(\rho\colon G\to\text{End}(V)\) of a simple algebraic group \(G\) over an algebraically closed field \(K\) there is the monoid \(M_\rho:=\overline{K^*\rho(G)}\subseteq\text{End}(V)\) and projective \(G\times G\)-embedding \(\mathbb P_\rho=[M_\rho\setminus\{0\}]/K^*\).
Lex E Renner
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A lattice theoretic characterization for the existence of a faithful irreducible representation [PDF]
International Journal of Group Theory, 2023 In a recent article S\'ebastien Palcoux formulated a sufficient condition on the subgroup lattice of a finite group $G$ that guarantees the existence of a faithful irreducible complex representation of $G$, and asked whether his condition is also ...
Peter Palfy
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Induced 3-Lie algebras, superalgebras and induced representations; pp. 116–133 [PDF]
Proceedings of the Estonian Academy of Sciences, 2020 We construct 3-Lie superalgebras on a commutative superalgebra by means of involution and even degree derivation. We construct a representation of induced 3-Lie algebras and superalgebras by means of a representation of initial (binary) Lie algebra ...
Priit Lätt, Viktor Abramov
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Algebra with ternary cyclic relations, representations and quark model [PDF]
Proceedings of the Estonian Academy of Sciences, 2023 We propose a unital associative algebra, motivated by a generalization of the Pauliâs exclusion principle proposed for the quark model. The generators of this algebra satisfy the following relations: The sum of squares of all generators is equal to ...
Viktor Abramov +2 more
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On families of twisted power partial isometries
Karpatsʹkì Matematičnì Publìkacìï, 2022 We consider families of power partial isometries satisfying twisted commutation relations with deformation parameters $\lambda_{ij}\in\mathbb C$, $|\lambda_{ij}|=1$.
V.L. Ostrovskyi +2 more
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Lagrangian formulation for free 6D infinite spin field
Nuclear Physics B, 2023 We construct a Lagrangian that describes the dynamics of a six-dimensional free infinite (continuous) spin field in 6D Minkowski space. The Lagrangian is formulated in the framework of the BRST approach to higher spin field theory and is based on a ...
I.L. Buchbinder +3 more
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Kronecker coefficients: the tensor square conjecture and unimodality [PDF]
Discrete Mathematics & Theoretical Computer Science, 2014 We consider two aspects of Kronecker coefficients in the directions of representation theory and combinatorics. We consider a conjecture of Jan Saxl stating that the tensor square of the $S_n$-irreducible representation indexed by the staircase partition
Igor Pak, Greta Panova, Ernesto Vallejo
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Induced operators on the generalized symmetry classes of tensors [PDF]
International Journal of Group Theory, 2021 Let $V$ be a unitary space. Suppose $G$ is a subgroup of the symmetric group of degree $m$ and $\Lambda$ is an irreducible unitary representation of $G$ over a vector space $U$.
Gholamreza Rafatneshan, Yousef Zamani
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GENERICALLY FREE REPRESENTATIONS II: IRREDUCIBLE REPRESENTATIONS [PDF]
Transformation Groups, 2020 We determine which faithful irreducible representations $V$ of a simple linear algebraic group $G$ are generically free for Lie($G$), i.e., which $V$ have an open subset consisting of vectors whose stabilizer in Lie($G$) is zero. This relies on bounds on $\dim V$ obtained in prior work (part I), which reduce the problem to a finite number of ...
Garibaldi, Skip, Guralnick, Robert M.
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The unitary representations of the Poincar\'e group in any spacetime dimension
SciPost Physics Lecture Notes, 2021 An extensive group-theoretical treatment of linear relativistic field equations on Minkowski spacetime of arbitrary dimension $D\geqslant 3$ is presented.
Xavier Bekaert, Nicolas Boulanger
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