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Displaying 41 – 60 of 1248

A problem of Kollár and Larsen on finite linear groups and crepant resolutions

Robert Guralnick, Pham Tiep (2012)

Journal of the European Mathematical Society

The notion of age of elements of complex linear groups was introduced by M. Reid and is of importance in algebraic geometry, in particular in the study of crepant resolutions and of quotients of Calabi–Yau varieties. In this paper, we solve a problem raised by J. Kollár and M. Larsen on the structure of finite irreducible linear groups generated by elements of age $\leq 1$ . More generally, we bound the dimension of finite irreducible linear groups generated by elements of bounded deviation. As a consequence...

A property of special representations of Weyl groups.

N. Spaltenstein (1983)

Journal für die reine und angewandte Mathematik

À propos d’un lemme de Ribet

Joël Bellaïche (2003)

Rendiconti del Seminario Matematico della Università di Padova

A rank 3 tangent complex of ${PSp}_{4} (q)$ , $q$ odd.

Sarli, John, McClurg, Phillip (2001)

Advances in Geometry

A remark on the irreducible characters and fake degrees of finite real reflection groups.

E.M. Opdam (1995)

Inventiones mathematicae

A restriction theorem and the Poincare series for U-invariants.

Dmitri I. Panyushev (1995)

Mathematische Annalen

A simple matrix semigroup which is not completely simple.

A.V. Kelarev (1988)

Semigroup forum

A Specialization Theorem for Certain Weyl Group Representations and an Application to the Green Polynomials of Unitary Groups.

R. Hotta, T.A. Springer (1977)

Inventiones mathematicae

A splitting theorem for linear polycyclic groups.

Abels, Herbert, Alperin, Roger C. (2009)

The New York Journal of Mathematics [electronic only]

A Stiefel complex for the orthogonal group of a field.

K. Vogtmann (1982)

Commentarii mathematici Helvetici

A symplectic representation of $E_{7}$

Tevian Dray, Corinne A. Manogue, Robert A. Wilson (2014)

Commentationes Mathematicae Universitatis Carolinae

We explicitly construct a particular real form of the Lie algebra $𝔢_{7}$ in terms of symplectic matrices over the octonions, thus justifying the identifications $𝔢_{7} ≅ 𝔰𝔭 (6, 𝕆)$ and, at the group level, $E_{7} ≅ Sp (6, 𝕆)$ . Along the way, we provide a geometric description of the minimal representation of $𝔢_{7}$ in terms of rank 3 objects called cubies.

A Theorem on the Restriction of Group Characters, and Its Application to the Character Theory of SL (n, q).

M.T. Karkar, J.A. Green (1975)

Mathematische Annalen

A third look at weight diagrams

Nikolai Vavilov (2000)

Rendiconti del Seminario Matematico della Università di Padova

A transvection decomposition in GL(n,2)

Clorinda De Vivo, Claudia Metelli (2002)

Colloquium Mathematicae

An algorithm is given to decompose an automorphism of a finite vector space over ℤ₂ into a product of transvections. The procedure uses partitions of the indexing set of a redundant base. With respect to tents, i.e. finite ℤ₂-representations generated by a redundant base, this is a decomposition into base changes.

A tropical view on Bruhat-Tits buildings and their compactifications

Annette Werner (2011)

Open Mathematics

We relate some features of Bruhat-Tits buildings and their compactifications to tropical geometry. If G is a semisimple group over a suitable non-Archimedean field, the stabilizers of points in the Bruhat-Tits building of G and in some of its compactifications are described by tropical linear algebra. The compactifications we consider arise from algebraic representations of G. We show that the fan which is used to compactify an apartment in this theory is given by the weight polytope of the representation...

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