Invariant theory for a parabolic subgroup of 𝑆𝐿(𝑛+1,𝑅)

Gover, A. Rod

doi:10.1090/S0002-9939-1995-1231035-5

Invariant theory for a parabolic subgroup of $\textrm {SL}(n+1,\textbf {R})$
HTML articles powered by AMS MathViewer

by A. Rod Gover

Proc. Amer. Math. Soc. 123 (1995), 1543-1553

DOI: https://doi.org/10.1090/S0002-9939-1995-1231035-5

PDF | Request permission

Abstract:

For a certain maximal parabolic P of ${\text {SL}}(n + 1,\mathbb {R})$, the complete invariant theory is presented for a class of P-representation modules. These modules arise naturally from the geometry of ${\mathbb {P}^n}$. In particular, a means of listing all the exceptional invariants is described. This is a model problem for some parabolic invariant theory problems posed by Fefferman.

References

Toby N. Bailey, Michael G. Eastwood, and C. Robin Graham, Invariant theory for conformal and CR geometry, Ann. of Math. (2) 139 (1994), no. 3, 491–552. MR 1283869, DOI 10.2307/2118571
Toby N. Bailey and A. Rod Gover, Exceptional invariants in the parabolic invariant theory of conformal geometry, Proc. Amer. Math. Soc. 123 (1995), no. 8, 2535–2543. MR 1243161, DOI 10.1090/S0002-9939-1995-1243161-5
Michael G. Eastwood and C. Robin Graham, Invariants of conformal densities, Duke Math. J. 63 (1991), no. 3, 633–671. MR 1121149, DOI 10.1215/S0012-7094-91-06327-1
Charles Fefferman, Parabolic invariant theory in complex analysis, Adv. in Math. 31 (1979), no. 2, 131–262. MR 526424, DOI 10.1016/0001-8708(79)90025-2
A. Rod Gover, Invariants on projective space, J. Amer. Math. Soc. 7 (1994), no. 1, 145–158. MR 1214703, DOI 10.1090/S0894-0347-1994-1214703-8

Invariants and calculus for projective geometries

C. Robin Graham, Invariant theory of parabolic geometries, Complex geometry (Osaka, 1990) Lecture Notes in Pure and Appl. Math., vol. 143, Dekker, New York, 1993, pp. 53–66. MR 1201601
Anthony W. Knapp, Lie groups, Lie algebras, and cohomology, Mathematical Notes, vol. 34, Princeton University Press, Princeton, NJ, 1988. MR 938524
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