Displaying similar documents to “Degenerate principal series representations of S p ( 2 n , 𝐑 ) ”

On the power-series expansion of a rational function

D. V. Lee (1992)

Acta Arithmetica

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Introduction. The problem of determining the formula for P S ( n ) , the number of partitions of an integer into elements of a finite set S, that is, the number of solutions in non-negative integers, h s ₁ , . . . , h s k , of the equation hs₁ s₁ + ... + hsk sk = n, was solved in the nineteenth century (see Sylvester [4] and Glaisher [3] for detailed accounts). The solution is the coefficient of x ⁿ i n [(1-xs₁)... (1-xsk)]-1, expressions for which they derived. Wright [5] indicated a simpler method by which to find part...

Representations of s ⁢ l q ⁢ 3 at the roots of unity

Nicoletta Cantarini (1996)

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni

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In this paper we study the irreducible finite dimensional representations of the quantized enveloping algebra U q ⁢ g associated to g = s ⁢ l ⁢ 3 , at the roots of unity. It is known that these representations are parametrized, up to isomorphisms, by the conjugacy classes of the group G = S ⁢ L ⁢ 3 . We get a complete classification of the representations corresponding to the submaximal unipotent conjugacy class and therefore a proof of the De Concini-Kac conjecture about the dimension of the U q ⁢ g -modules at the roots...