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- W1987325913 abstract "Let [inline-graphic xmlns:xlink=http://www.w3.org/1999/xlink xlink:href=01i /] = [inline-graphic xmlns:xlink=http://www.w3.org/1999/xlink xlink:href=02i /] or [inline-graphic xmlns:xlink=http://www.w3.org/1999/xlink xlink:href=03i /], and let G = U(p, q; [inline-graphic xmlns:xlink=http://www.w3.org/1999/xlink xlink:href=04i /]) be the isometry group of a [inline-graphic xmlns:xlink=http://www.w3.org/1999/xlink xlink:href=05i /]-hermitian form of signature (p, q). For 2n ≤ min (p, q), we consider the action of G on Vn, the direct sum of n copies of the standard module V = [inline-graphic xmlns:xlink=http://www.w3.org/1999/xlink xlink:href=06i /], and the associated action of G on the regular part of the null cone, denoted by X00. We show that there is a commuting set of G-invariant differential operators acting on the space of C∞ functions on X00 which transform according to a distinguished GL(n, [inline-graphic xmlns:xlink=http://www.w3.org/1999/xlink xlink:href=07i /]) character, and the resulting kernel is an irreducible unitary representation of G. Our result can be interpreted as providing a geometric construction of the theta lift of the characters from the group G' = U(n, n) or O* (4n). The construction and approach here follow a previous work of Zhu and Huang [Representation Theory1 (1997)] where the group concerned is G = O(p, q) with p + q even." @default.
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- W1987325913 date "1998-01-01" @default.
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- W1987325913 title "On certain distinguished unitary representations supported on null cones" @default.
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- W1987325913 doi "https://doi.org/10.1353/ajm.1998.0043" @default.
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