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(g, K)-module of O(p, q) associated with the finite-dimensional representation of sl(2) 90263491 橋本, 隆司 ハシモト, タカシ Hashimoto, Takashi Electronic version of an article published as INTERNATIONAL JOURNAL OF MATHEMATICS, 2021, 32(2). https://doi.org/10.1142/S0129167X21500099. (C) World Scientific Publishing Company https://www.worldscientific.com/worldscinet/ijm Indefinite orthogonal group moment map on symplectic vector space canonical quantization irreducible (g K)-module K-type formula. Indefinite orthogonal group moment map on symplectic vector space canonical quantization irreducible (g K)-module K-type formula. The main aim of this paper is to show that one can construct (????,K)-modules of O(p,q) associated with the finite-dimensional representation of ????????2 by quantizing the moment map on the symplectic vector space (ℂp+q) ℝ and using the fact that (O(p,q),SL2(ℝ)) is a dual pair. Then one obtains the K-type formula, the Gelfand–Kirillov dimension and the Bernstein degree of them for all non-negative integers m satisfying m + 3 ≤ (p + q)/2 when p,q ≥ 2 and p + q is even. In fact, one finds that the Gelfand–Kirillov dimension is equal to p + q − 3 and the Bernstein degree is equal to 4(m + 1)(p + q − 4)!/((p − 2)!(q − 2)!). World Scientific Publishing 2021-02 eng journal article AM https://repository.lib.tottori-u.ac.jp/records/7223 10.1142/s0129167x21500099 Hashimoto Takashi. (g, K)-module of O(p, q) associated with the finite-dimensional representation of sl(2). INTERNATIONAL JOURNAL OF MATHEMATICS. 2021. 32(2). doi:10.1142/s0129167x21500099 0129167X INTERNATIONAL JOURNAL OF MATHEMATICS INTERNATIONAL JOURNAL OF MATHEMATICS 32 2 2150009 https://repository.lib.tottori-u.ac.jp/record/7223/files/ijm32(2)_s0129167x21500099.pdf application/pdf 374.3 kB 2023-03-17