Transcending classical invariant theory

Howe, Roger

doi:10.1090/S0894-0347-1989-0985172-6

Transcending classical invariant theory
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by Roger Howe

J. Amer. Math. Soc. 2 (1989), 535-552

DOI: https://doi.org/10.1090/S0894-0347-1989-0985172-6

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References

Pierre Cartier, Quantum mechanical commutation relations and theta functions, Algebraic Groups and Discontinuous Subgroups (Proc. Sympos. Pure Math., Boulder, Colo., 1965) Amer. Math. Soc., Providence, R.I., 1966, pp. 361–383. MR 0216825
Jacques Dixmier, Algèbres enveloppantes, Cahiers Scientifiques, Fasc. XXXVII, Gauthier-Villars Éditeur, Paris-Brussels-Montreal, Que., 1974 (French). MR 0498737
D. Flath, Decomposition of representations into tensor products, Automorphic forms, representations and $L$-functions (Proc. Sympos. Pure Math., Oregon State Univ., Corvallis, Ore., 1977) Proc. Sympos. Pure Math., XXXIII, Amer. Math. Soc., Providence, R.I., 1979, pp. 179–183. MR 546596
Stephen Gelbart, Holomorphic discrete series for the real symplectic group, Invent. Math. 19 (1973), 49–58. MR 320231, DOI 10.1007/BF01418850
Kenneth I. Gross and Ray A. Kunze, Bessel functions and representation theory. II. Holomorphic discrete series and metaplectic representations, J. Functional Analysis 25 (1977), no. 1, 1–49. MR 0453928, DOI 10.1016/0022-1236(77)90030-1
Sigurđur Helgason, Differential geometry and symmetric spaces, Pure and Applied Mathematics, Vol. XII, Academic Press, New York-London, 1962. MR 0145455
Roger Howe, Remarks on classical invariant theory, Trans. Amer. Math. Soc. 313 (1989), no. 2, 539–570. MR 986027, DOI 10.1090/S0002-9947-1989-0986027-X
R. Howe, $\theta$-series and invariant theory, Automorphic forms, representations and $L$-functions (Proc. Sympos. Pure Math., Oregon State Univ., Corvallis, Ore., 1977) Proc. Sympos. Pure Math., XXXIII, Amer. Math. Soc., Providence, R.I., 1979, pp. 275–285. MR 546602
Roger Howe, Quantum mechanics and partial differential equations, J. Functional Analysis 38 (1980), no. 2, 188–254. MR 587908, DOI 10.1016/0022-1236(80)90064-6
Richard V. Kadison, Remarks on the type of von Neumann algebras of local observables in quantum field theory, J. Mathematical Phys. 4 (1963), 1511–1516. MR 159585, DOI 10.1063/1.1703932
M. Kashiwara and M. Vergne, On the Segal-Shale-Weil representations and harmonic polynomials, Invent. Math. 44 (1978), no. 1, 1–47. MR 463359, DOI 10.1007/BF01389900
Colette Mœglin, Marie-France Vignéras, and Jean-Loup Waldspurger, Correspondances de Howe sur un corps $p$-adique, Lecture Notes in Mathematics, vol. 1291, Springer-Verlag, Berlin, 1987 (French). MR 1041060, DOI 10.1007/BFb0082712
S. Rallis, On the Howe duality conjecture, Compositio Math. 51 (1984), no. 3, 333–399. MR 743016
Masahiko Saito, Représentations unitaires des groupes symplectiques, J. Math. Soc. Japan 24 (1972), 232–251 (French). MR 299728, DOI 10.2969/jmsj/02420232
I. E. Segal, The complex-wave representation of the free boson field, Topics in functional analysis (essays dedicated to M. G. Kreĭn on the occasion of his 70th birthday), Adv. in Math. Suppl. Stud., vol. 3, Academic Press, New York-London, 1978, pp. 321–343. MR 538026
David Shale, Linear symmetries of free boson fields, Trans. Amer. Math. Soc. 103 (1962), 149–167. MR 137504, DOI 10.1090/S0002-9947-1962-0137504-6
David A. Vogan Jr., The algebraic structure of the representation of semisimple Lie groups. I, Ann. of Math. (2) 109 (1979), no. 1, 1–60. MR 519352, DOI 10.2307/1971266
André Weil, Sur certains groupes d’opérateurs unitaires, Acta Math. 111 (1964), 143–211 (French). MR 165033, DOI 10.1007/BF02391012
Hermann Weyl, The classical groups, Princeton Landmarks in Mathematics, Princeton University Press, Princeton, NJ, 1997. Their invariants and representations; Fifteenth printing; Princeton Paperbacks. MR 1488158