Gelfand Pairs and Spherical Functions
نویسنده
چکیده
This is a summary of the lectures delivered on Special Functions and Linear Representation of Lie Groups at the NSF-CBMS Research Conference at East Carolina University in March 5-9, 1979. The entire lectures will be published by the American Mathematical Society as a conference monograph in Mathematics.
منابع مشابه
Gelfand Pairs, Representation Theory of the Symmetric Group, and the Theory of Spherical Functions
This thesis gives an introduction to the study of Gelfand pairs and their applications. We begin with a brief introduction to the notion of a Gelfand pair and then move to some of the foundational results concerning Gelfand pairs. Next, we explore specific examples of Gelfand pairs, developing tools of independent interest as we progress. We find that consideration of a specific example of a Ge...
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Let S be a connected and simply connected unimodular solvable Lie group, K a connected compact group acting on S as automorphisms. We call the pair (K;S) a Gelfand pair if the Banach -algebra L 1 (KnKnS=K) of allK-biinvariant integrable functions on K n S is commutative. The assumption that (K;S) is a Gelfand pair prescribes the structure of S. For example, if (K;S) is a Gelfand pair, then S is...
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The symmetric group S2n and the hyperoctaheadral group Hn is a Gelfand triple for an arbitrary linear representation φ of Hn. Their φ-spherical functions can be caught as transition matrix between suitable symmetric functions and the power sums. We generalize this triplet in the term of wreath product. It is shown that our triplet are always to be a Gelfand triple. Furthermore we study the rela...
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The action of the unitary group on the real Heisenberg group yields a Gelfand pair. The associated spherical functions are well known and have been computed independently by many authors. In this paper we develop a discrete counterpart to this story by replacing the real numbers by a finite field of odd characteristic. This produces a finite Gelfand pair whose spherical functions are computed e...
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تاریخ انتشار 2004