Representations of the group $GL(n,F)$ where $F$ is a non-Archimedean local field
    
    
  
  
  
      
      
      
        
Trudy Matematicheskogo Instituta imeni V.A. Steklova, Tome 31 (1976) no. 3, pp. 1-68
    
  
  
  
  
  
    
      
      
        
      
      
      
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              			This article is a survey of recent results in the theory of representations of reductive $\wp$-adic groups. For simplicity of presentation only the groups $GL(n)$ are treated. Chapter I provides general information on representations of locally compact zero-dimensional groups. Chapter II presents Harish-Chandra's method of studying the representations of $GL(n)$, which is based on reduction to cuspidal representations. Some finiteness theorems are proved by this method. In Chapter III we study another approach to the representations of $GL(n)$, due to Gel'fand and Kazhdan; it is based on restricting the representations from $GL(n)$ to a subgroup $P_n$. All theorems are presented with detailed proofs. No prior information is assumed on the part of the reader except the most elementary familiarity with the structure of non-Archimedean local fields.
			
            
            
            
          
        
      @article{RM_1976_31_3_a0,
     author = {J. H. Bernstein and A. V. Zelevinskii},
     title = {Representations of the group $GL(n,F)$ where $F$ is a {non-Archimedean} local field},
     journal = {Trudy Matematicheskogo Instituta imeni V.A. Steklova},
     pages = {1--68},
     publisher = {mathdoc},
     volume = {31},
     number = {3},
     year = {1976},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/RM_1976_31_3_a0/}
}
                      
                      
                    TY - JOUR AU - J. H. Bernstein AU - A. V. Zelevinskii TI - Representations of the group $GL(n,F)$ where $F$ is a non-Archimedean local field JO - Trudy Matematicheskogo Instituta imeni V.A. Steklova PY - 1976 SP - 1 EP - 68 VL - 31 IS - 3 PB - mathdoc UR - http://geodesic.mathdoc.fr/item/RM_1976_31_3_a0/ LA - en ID - RM_1976_31_3_a0 ER -
%0 Journal Article %A J. H. Bernstein %A A. V. Zelevinskii %T Representations of the group $GL(n,F)$ where $F$ is a non-Archimedean local field %J Trudy Matematicheskogo Instituta imeni V.A. Steklova %D 1976 %P 1-68 %V 31 %N 3 %I mathdoc %U http://geodesic.mathdoc.fr/item/RM_1976_31_3_a0/ %G en %F RM_1976_31_3_a0
J. H. Bernstein; A. V. Zelevinskii. Representations of the group $GL(n,F)$ where $F$ is a non-Archimedean local field. Trudy Matematicheskogo Instituta imeni V.A. Steklova, Tome 31 (1976) no. 3, pp. 1-68. http://geodesic.mathdoc.fr/item/RM_1976_31_3_a0/
