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Book Review: Characters and blocks of finite groups

2000
*
Bulletin of the American Mathematical Society
*

Modular

doi:10.1090/s0273-0979-00-00854-5
fatcat:aqpbszfwkzhfvmplrvknziogdm
*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*. ...##
###
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

2010
*
Mathematics of Computation
*

Let G be a

doi:10.1090/s0025-5718-10-02330-6
fatcat:ss2ot3jeefcbpi4e23snefv5iu
*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. ...##
###
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]

2018
*
arXiv
*
pre-print

We describe two methods for

arXiv:1809.07647v1
fatcat:5zred2pgc5emrmbjq4l36j45dy
*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. ...##
###
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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