Rad HAZU, Matematičke znanosti, Vol. 28 (2024), 193-222.

SIMILITUDE EXCEPTIONAL THETA CORRESPONDENCES

Petar Bakić, Wee Teck Gan and Gordan Savin

Department of Mathematics, National University of Singapore, 10 Lower Kent Ridge Road, Singapore 119076
e-mail: matgwt@nus.edu.sg

Abstract.   We describe a systematic way of constructing dual pairs of similitude groups. We study the theta correspondences arising in this way and prove that Howe duality holds for the similitude dual pair if and only if it holds for the original reductive dual pair used in our construction. Several examples of exceptional correspondences are discussed.

2020 Mathematics Subject Classification.   11S90, 17A75, 17C40.

Key words and phrases.   theta correspondences, similitude groups.

DOI: https://doi.org/10.21857/mnlqgc3qqy

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