Highest weight modules for Hermitian symmetric pairs of exceptional type

Enright, Thomas J.; Shelton, Brad

doi:10.1090/S0002-9939-1989-0961404-7

Highest weight modules for Hermitian symmetric pairs of exceptional type
HTML articles powered by AMS MathViewer

by Thomas J. Enright and Brad Shelton PDF

Proc. Amer. Math. Soc. 106 (1989), 807-819 Request permission

Abstract:

We analyze the categories of highest weight modules with a semiregular generalized infinitesimal character for the two exceptional Hermitian symmetric cases. These categories are completely described, and, as a consequence, we see that the combinatorial description of the general (regular integral) categories of highest weight modules previously given in the classical cases holds also in the exceptional cases.

References

Brian D. Boe, Thomas J. Enright, and Brad Shelton, Determination of the intertwining operators for holomorphically induced representations of Hermitian symmetric pairs, Pacific J. Math. 131 (1988), no. 1, 39–50. MR 917864
David H. Collingwood, Ronald S. Irving, and Brad Shelton, Filtrations on generalized Verma modules for Hermitian symmetric pairs, J. Reine Angew. Math. 383 (1988), 54–86. MR 921987, DOI 10.1515/crll.1988.383.54
Thomas J. Enright and Brad Shelton, Decompositions in categories of highest weight modules, J. Algebra 100 (1986), no. 2, 380–402. MR 840583, DOI 10.1016/0021-8693(86)90083-9
Thomas J. Enright and Brad Shelton, Categories of highest weight modules: applications to classical Hermitian symmetric pairs, Mem. Amer. Math. Soc. 67 (1987), no. 367, iv+94. MR 888703, DOI 10.1090/memo/0367
Brad Shelton, Extensions between generalized Verma modules: the Hermitian symmetric cases, Math. Z. 197 (1988), no. 3, 305–318. MR 926843, DOI 10.1007/BF01418333
David A. Vogan Jr., A generalized $\tau$-invariant for the primitive spectrum of a semisimple Lie algebra, Math. Ann. 242 (1979), no. 3, 209–224. MR 545215, DOI 10.1007/BF01420727