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Book Review: Characters and blocks of finite groups

David Gluck
2000 Bulletin of the American Mathematical Society  
Modular representation theory (also called block theory) studies the modular representations of a finite group G and their relation to the ordinary representations of G.  ...  One goal that is not reasonable for infinite families is to compute the values of the irreducible Brauer characters; very little has been done in this direction even for the symmetric groups.  ... 
doi:10.1090/s0273-0979-00-00854-5 fatcat:aqpbszfwkzhfvmplrvknziogdm

Page 4824 of Mathematical Reviews Vol. , Issue 85k [page]

1985 Mathematical Reviews  
The calculation of the 2-modular characters of finite groups using a computer is described.  ...  Let B be a p-block of G with defect group D and let k,/ and k; denote the numbers of ordinary and modular irreducible charac- ters in B and the number of ordinary irreducibles with height 2, respectively  ... 

Page 3993 of Mathematical Reviews Vol. , Issue 2000f [page]

2000 Mathematical Reviews  
The aim of this paper is to check two of the most tempting conjectures of modular representation theory of finite groups: Alperin’s weight conjecture and Dade’s ordinary conjecture, for the sporadic simple  ...  This allows one to use tools from computational group theory and computational character theory, together with a detailed knowl- edge of the structure of the maximal subgroups of Co3, to classify the radical  ... 

Page 3370 of Mathematical Reviews Vol. , Issue 96f [page]

1996 Mathematical Reviews  
The dual result on conjugacy classes is a description of finite groups G with an ordinary irreducible character y and an element g € G such that y(y) =0 for every nonidentity y which is conjugate neither  ...  96f:20010 describes finite groups G with an ordinary irreducible character yx and an element g € G such that €(g) = 0 for all € € Irr(G) — {le, x, 7%}.  ... 

Page 5287 of Mathematical Reviews Vol. , Issue 99h [page]

1999 Mathematical Reviews  
a new algorithm for computing matrices of standard orthogonal irreducible representations of symmetric groups.  ...  Maximal subgroups, presentations and ordinary irreducible char- acters for some simple groups and their decorations are collected in [J. H. Conway et al., Atlas of finite groups, Oxford Univ.  ... 

Computing matrix representations

Vahid Dabbaghian, John D. Dixon
2010 Mathematics of Computation  
Let G be a finite group and χ a faithful irreducible character for G.  ...  Earlier papers by the first author describe techniques for computing a matrix representation for G which affords χ whenever the degree χ(1) is less than 32.  ...  Acknowledgements We wish to acknowledge the thoughtful suggestions of an anonymous referee, and particularly for the construction referred to in Section 2.  ... 
doi:10.1090/s0025-5718-10-02330-6 fatcat:ss2ot3jeefcbpi4e23snefv5iu

Page 5346 of Mathematical Reviews Vol. , Issue 91J [page]

1991 Mathematical Reviews  
Finally the techniques can be used to compute the degrees of the irreducible representations of a twisted group algebra on G.  ...  From the text of the translation: “The problem of existence of p- blocks of defect 0 in a finite group was posed by Richard Brauer, the founder of the theory of modular representations of finite groups  ... 

Page 781 of Mathematical Reviews Vol. 36, Issue 4 [page]

1968 Mathematical Reviews  
Finally, the author considers irreducible ordinary representations of @ which are associated with respect to a normal subgroup ® of @ in the sense of A. H.  ...  The author presents some results in the theory of projec- tive representations of a finite group over the field of complex numbers.  ... 

Turning Weight Multiplicities into Brauer Characters [article]

Frank Lübeck
2018 arXiv   pre-print
We describe two methods for computing p-modular Brauer character tables for groups of Lie type G(p^f) in defining characteristic p, assuming that the ordinary character table of G(p^f) is known, and the  ...  weight multiplicities of the corresponding algebraic group G are known for p-restricted highest weights.  ...  The irreducible representations of G(q) over F p (called defining characteristic representations) are restrictions of irreducible representations of the algebraic group G.  ... 
arXiv:1809.07647v1 fatcat:5zred2pgc5emrmbjq4l36j45dy

Page 5684 of Mathematical Reviews Vol. , Issue 90J [page]

1990 Mathematical Reviews  
a bijection between the b € T'Y, and the irreducible negative G- representations which on restriction to Kero remain irreducible.  ...  Using known techniques for restricting the irreducible ordinary representations of O(m,R) to S,, the au- thors show that the above problem is reduced to determining the inner product of the basic spin  ... 

Page 1680 of Mathematical Reviews Vol. , Issue 2002C [page]

2002 Mathematical Reviews  
Proceedings of the Summer School on Representation Theory of Algebras, Finite and Reductive Groups (Cluj-Napoca, 1997), 67-100, Babes-Bolyai Univ. Fac. Math. Comput. Sci. Res.  ...  This con- struction was inspired by some ideas in work of Molchanov on ordinary representations of symmetric groups.  ... 

Page 6260 of Mathematical Reviews Vol. , Issue 90K [page]

1990 Mathematical Reviews  
The author presents a computation of the values of all primitive permutation characters of Held’s sporadic simple group together with their decompositions as sums of irreducible complex charac- ters.  ...  ,) as compositions | oa &; *, GL(V) where €,-_, is the multiplicative group of a Clifford algebra and p is an irreducible representation thereof.  ... 

Page 2319 of Mathematical Reviews Vol. , Issue 2001D [page]

2001 Mathematical Reviews  
The necessary computations with ordinary characters of finite groups of Lie type and of Weyl groups are done using the computer algebra systems CHEVIE and GAP.  ...  Denote by ®2 the automorphism group of the free group F) on two generators. The object of the article is the classification of all indecomposable complex linear representations of ®) of degree < 5.  ... 

Page 3673 of Mathematical Reviews Vol. , Issue 92g [page]

1992 Mathematical Reviews  
3673 ticular he gave g-analogues of classical results of Green on modular representations of finite groups.  ...  (D-AACH-DM) Computational aspects of representation theory of finite groups. Representation theory of finite groups and finite-dimensional algebras (Bielefeld, 1991), 37-64, Progr.  ... 

Page 805 of Mathematical Reviews Vol. , Issue 98B [page]

1998 Mathematical Reviews  
This algorithm is a modified version of the O(|G| log|G|) algo- rithm for computing ordinary irreducible representations of super- solvable groups due to U. Baum and M. Clausen [Math.  ...  [Shokrollahi, Mohammad Amin] (D-BONN-IF; Bonn) Computing irreducible representations of supersolvable groups over small finite fields. (English summary) Math. Comp. 66 (1997), no. 218, 779-786.  ... 
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