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Individual differences shape conceptual representation in the brain
Visconti di Oleggio Castello M +2 more
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UNIPOTENT ELEMENTS IN REPRESENTATIONS OF FINITE GROUPS OF LIE TYPE
Journal of Algebra and Its Applications, 2012Let G be a finite quasi-simple group of Lie type of defining characteristic r > 2. Let H = 〈h, G〉 be a group with normal subgroup G, where h is a non-central r-element of H. Let ϕ be an irreducible representation of H non-trivial on G over an algebraically closed field of characteristic ℓ ≠ r. We show that ϕ(h) has at least two distinct eigenvalues
Di Martino, L., Zalesski, A. E.
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Representations and maximal subgroups of finite groups of Lie type
Geometriae Dedicata, 1988Let σ be an endomorphism of a simple, simply connected, algebraic group $$\[\bar G\]$$ over K, where K is the algebraic closure of Fp, and assume the fixed point group G = $$ {\text{G = }}{\overline {\text{G}} _{\sigma }} $$ is finite and quasisimple.
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Mod p Reducibility of Unramified Representations of Finite Groups of Lie Type
Proceedings of the London Mathematical Society, 2002Let \(G\) be a finite group of Lie type in prime characteristic \(p\) and let \(\chi\) be an irreducible complex character of \(G\). A basic question in the representation theory of \(G\) is to decide whether or not \(\chi\) is irreducible modulo \(p\).
Tiep, Pham Huu, Zalesskij, A. E.
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Representations of Heeke Algebras and Finite Groups of Lie Type
1999R. Brauer posed in his famous lectures on modern mathematics 1963 more than 40 problems, questions and conjectures about the representation theory of finite groups, cf. [10]. These questions have had a big influence on the development of the theory since then. Most of the problems may be summarized under the following central question.
Richard Dipper +3 more
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Modular Representations of Finite Groups of Lie Type
2005Finite groups of Lie type encompass most of the finite simple groups. Their representations and characters have been studied intensively for half a century, though some key problems remain unsolved. This is the first comprehensive treatment of the representation theory of finite groups of Lie type over a field of the defining prime characteristic. As a
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Communications in Algebra, 2000
Absolutely irreducible representations of finite groups of exceptional Lie types in defining characteristic whose images contain matrices with simple spectra are determined. The term ”simple spectrum“ means that each eigenvalue has multiplicity 1. The similar question for the classical finite groups has been solved in the authors' previous paper [Comm.
I.D. Suprunenko, A.E. Zalesskii
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Absolutely irreducible representations of finite groups of exceptional Lie types in defining characteristic whose images contain matrices with simple spectra are determined. The term ”simple spectrum“ means that each eigenvalue has multiplicity 1. The similar question for the classical finite groups has been solved in the authors' previous paper [Comm.
I.D. Suprunenko, A.E. Zalesskii
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Modular Representations of Finite Groups of Lie Type in Non-defining Characteristic
1997Let us consider a connected reductive algebraic group G, defined over the finite field F q with corresponding Frobenius morphism F. We are concerned here with properties of finite-dimensional modules for the finite group G F over a sufficiently large field k of characteristic l where l is a prime not dividing q.
Meinolf Geck, Gerhard Hiss
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Modular Representations of Finite Groups of Lie Type
Proceedings of the London Mathematical Society, 1976Carter, R. W., Lusztig, G.
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