Communications of the Korean Mathematical Society (대한수학회논문집)
- Volume 9 Issue 3
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- Pages.521-529
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- 1994
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- 1225-1763(pISSN)
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- 2234-3024(eISSN)
UNITARY SERIES OF $GL_2(R)$ AND $GL_2(C)$
- Kim, Seon-Ja (Department of Mathematics, Inha University, Incheon 402-751)
- Published : 1994.07.01
Abstract
This paper studies the realization of irreducible unitary representations of $GL_2(R)$ and $GL_2(C)$ by Bargmann's classification[1]. Since the representations of general matrix groups can be obtained by the extensions of characters of a special linear group, we shall follow to a large extent the pattern of the results in [5], [6], and [8]. This article is divided into two sections. In the first section we describe the realization of principal series and discrete series and complementary series of $GL_2(R)$. The last section is devoted to the derivation of principal series and complementary series of $GL_2(C).
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