scholarly journals PHYSICAL METHODS OF GROUP REPRESENTATION THEORY (Ⅰ)——A NEW APPROACH TO THE THEORY OF FINITE GROUP REPRESENTATIONS

1977 ◽  
Vol 26 (4) ◽  
pp. 307
Author(s):  
CHEN JIN-QUAN ◽  
WANG FAN ◽  
GAO MEI-JUAN
Keyword(s):  
Finite Group ◽  
Representation Theory ◽  
Group Representation ◽  
Group Representations ◽  
New Approach ◽  
Group Representation Theory ◽  
Physical Methods

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.

On Extending Projectives of Finite Group-Graded Algebras

1991 ◽  
Vol 34 (2) ◽  
pp. 224-228
Author(s):  
Morton E. Harris
Keyword(s):  
Finite Group ◽  
Representation Theory ◽  
Group Representation ◽  
Sufficient Conditions ◽  
Projective Cover ◽  
Graded Algebras ◽  
Finite Dimensional ◽  
Completely Reducible ◽  
A Finite Group ◽  
Necessary And Sufficient

AbstractLet G be a finite group, let k be a field and let R be a finite dimensional fully G-graded k-algebra. Also let L be a completely reducible R-module and let P be a projective cover of R. We give necessary and sufficient conditions for P|R1 to be a projective cover of L|R1 in Mod (R1). In particular, this happens if and only if L is R1-projective. Some consequences in finite group representation theory are deduced.

scholarly journals Stratifications and Mackey Functors II: Globally Defined Mackey Functors

2010 ◽  
Vol 6 (1) ◽  
pp. 99-170 ◽  
Author(s):  
Peter Webb
Keyword(s):  
Representation Theory ◽  
Structural Properties ◽  
Characteristic Zero ◽  
Group Representation ◽  
Cartan Matrix ◽  
Weight Category ◽  
Group Representation Theory ◽  
Stratification Theory ◽  
Highest Weight ◽  
Mackey Functors

AbstractWe describe structural properties of globally defined Mackey functors related to the stratification theory of algebras. We show that over a field of characteristic zero they form a highest weight category and we also determine precisely when this category is semisimple. This approach is used to show that the Cartan matrix is often symmetric and non-singular, and we are able to compute finite parts of it in some instances. We also develop a theory of vertices of globally defined Mackey functors in the spirit of group representation theory, as well as giving information about extensions between simple functors.

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