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Classification of irreducible based modules over the complex representation ring of $ S_4 $
AIMS MathematicsThe complex representation rings of finite groups are the fundamental class of fusion rings, categorified by the corresponding fusion categories of complex representations.
Wenxia Wu, Yunnan Li
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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 [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 ...
Viktor Abramov, Priit Lätt
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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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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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Gelfand Models for Diagram Algebras [PDF]
Discrete Mathematics & Theoretical Computer Science, 2013 A Gelfand model for a semisimple algebra $\mathsf{A}$ over $\mathbb{C}$ is a complex linear representation that contains each irreducible representation of $\mathsf{A}$ with multiplicity exactly one.
Tom Halverson
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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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MASALAH EIGEN DAN EIGENMODE MATRIKS ATAS ALJABAR MIN-PLUS
Barekeng, 2021 Eigen problems and eigenmode are important components related to square matrices. In max-plus algebra, a square matrix can be represented in the form of a graph called a communication graph.
Eka Widia Rahayu +2 more
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