Several Questions About Finite Group Representations and Their Applications

1996 ◽  
pp. 31-40
Author(s):  
Yun Fan
Keyword(s):  
Finite Group ◽  
Group Representations

On the labelling and symmetry adaptation of the solvable finite group representations

1988 ◽  
Vol 21 (6) ◽  
pp. 1321-1328 ◽  
Author(s):  
S R A Nogueira ◽  
A O Caride ◽  
S I Zanette
Keyword(s):  
Finite Group ◽  
Group Representations ◽  
Symmetry Adaptation

scholarly journals Frame vector multipliers for finite group representations

2017 ◽  
Vol 519 ◽  
pp. 191-207 ◽  
Author(s):  
Zhongyan Li ◽  
Deguang Han
Keyword(s):  
Finite Group ◽  
Group Representations

scholarly journals Mapping class group representations from Drinfeld doubles of finite groups

2020 ◽  
Vol 29 (05) ◽  
pp. 2050033
Author(s):  
Jens Fjelstad ◽  
Jürgen Fuchs
Keyword(s):  
Finite Group ◽  
Finite Groups ◽  
Class Group ◽  
Marked Point ◽  
Mapping Class ◽  
Group Representations ◽  
Torelli Group ◽  
Group Data ◽  
A Finite Group ◽  
Marked Points

We investigate representations of mapping class groups of surfaces that arise from the untwisted Drinfeld double of a finite group [Formula: see text], focusing on surfaces without marked points or with one marked point. We obtain concrete descriptions of such representations in terms of finite group data. This allows us to establish various properties of these representations. In particular, we show that they have finite images, and that for surfaces of genus at least [Formula: see text] their restriction to the Torelli group is non-trivial if and only if [Formula: see text] is non-abelian.

scholarly journals Critical groups for Hopf algebra modules

2018 ◽  
Vol 168 (3) ◽  
pp. 473-503
Author(s):  
DARIJ GRINBERG ◽  
JIA HUANG ◽  
VICTOR REINER
Keyword(s):  
Finite Group ◽  
Hopf Algebra ◽  
Regular Representation ◽  
Critical Group ◽  
Critical Groups ◽  
Greatest Common Divisor ◽  
Group Representations ◽  
Finite Dimensional ◽  
Projective Representations ◽  
Finite Dimensional Hopf Algebra

AbstractThis paper considers an invariant of modules over a finite-dimensional Hopf algebra, called the critical group. This generalises the critical groups of complex finite group representations studied in [1, 11]. A formula is given for the cardinality of the critical group generally, and the critical group for the regular representation is described completely. A key role in the formulas is played by the greatest common divisor of the dimensions of the indecomposable projective representations.

J-Equivalence of group representations

1971 ◽  
Vol 70 (1) ◽  
pp. 9-14 ◽  
Author(s):  
V. P. Snaith
Keyword(s):  
Finite Group ◽  
Galois Group ◽  
Complex Representation ◽  
Group Representations ◽  
Root Of Unity ◽  
Representation Ring ◽  
A Finite Group

If G is a finite group of order N and ΓN is the Galois group of Q(w) over Q, where w is a primitive Nth root of unity then ΓN acts on the complex representation ring, R(G), of G. The group of co-invariants is denoted by R(G)ΓN = R(G)/W(G).

scholarly journals Orbifolds and finite group representations

2001 ◽  
Vol 26 (11) ◽  
pp. 649-669
Author(s):  
Li Chiang ◽  
Shi-Shyr Roan
Keyword(s):  
Finite Group ◽  
Abelian Group ◽  
Representation Theory ◽  
Hilbert Scheme ◽  
Group Representation ◽  
Quotient Singularity ◽  
Group Representations ◽  
Group Representation Theory ◽  
Crepant Resolutions

We present our recent understanding on resolutions of Gorenstein orbifolds, which involves the finite group representation theory. We concern only the quotient singularity of hypersurface type. The abelian groupAr(n)forA-type hypersurface quotient singularity of dimensionnis introduced. Forn=4, the structure of Hilbert scheme of group orbits and crepant resolutions ofAr(4)-singularity are obtained. The flop procedure of4-folds is explicitly constructed through the process.

Classification of Finite Group-Frames and Super-Frames

2007 ◽  
Vol 50 (1) ◽  
pp. 85-96 ◽  
Author(s):  
Deguang Han
Keyword(s):  
Finite Group ◽  
Equivalence Classes ◽  
Group Representations ◽  
Exact Number ◽  
A Finite Group ◽  
Frame Representations

AbstractGiven a finite group G, we examine the classification of all frame representations of G and the classification of all G-frames, i.e., frames induced by group representations of G. We show that the exact number of equivalence classes of G-frames and the exact number of frame representations can be explicitly calculated. We also discuss how to calculate the largest number L such that there exists an L-tuple of strongly disjoint G-frames.

scholarly journals Spherical designs and finite group representations (some results of E. Bannai)

2004 ◽  
Vol 25 (2) ◽  
pp. 213-227 ◽  
Author(s):  
Pierre de la Harpe ◽  
Claude Pache
Keyword(s):  
Finite Group ◽  
Group Representations ◽  
Spherical Designs
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