On minuscule representations, plane partitions and involutions in complex Lie groups

Duke Mathematical Journal - Tập 73 Số 2 - 1994
John R. Stembridge

Tóm tắt

Từ khóa


Tài liệu tham khảo

[B] N. Bourbaki, <i>Groupes et Algèbres de Lie, Chap. IV–VI</i>, Masson, Paris, 1981.

[H1] J. E. Humphreys, <i>Introduction to Lie Algebras and Representation Theory</i>, Springer-Verlag, Berlin, 1972.

[H2] J. E. Humphreys, <i>Linear Algebraic Groups</i>, Springer-Verlag, Berlin, 1975.

[K] B. Kostant, <i>The principal three-dimensional subgroup and the Betti numbers of a complex simple Lie group</i>, Amer. J. Math. <b>81</b> (1959), 973–1032.

[Ku] G. Kuperberg, <i>Self-complementary plane partitions by Proctor's method</i>, preprint.

[M] I. G. Macdonald, <i>Symmetric Functions and Hall Polynomials</i>, Oxford University Press, Oxford, 1979.

[MRR] W. H. Mills, D. P. Robbins, and H. Rumsey, <i>Self-complementary totally symmetric plane partitions</i>, J. Combin. Theory Ser. A <b>42</b> (1986), no. 2, 277–292.

[P] R. A. Proctor, <i>Bruhat lattices, plane partition generating functions, and minuscule representations</i>, European J. Combin. <b>5</b> (1984), no. 4, 331–350.

[S] C. S. Seshadri, <i>Geometry of $G/P$—I. Theory of standard monomials for minuscule representations</i>, C. P. Ramanujam—A Tribute, Tata Inst. Fund. Res. Studies in Math., vol. 8, Springer-Verlag, Berlin, 1978, pp. 207–239.

[St1] R. P. Stanley, <i>Enumerative Combinatorics, Vol. I</i>, The Wadsworth &amp; Brooks/Cole Mathematics Series, Wadsworth and Brooks/Cole, Monterey, California, 1986.

[St2] R. P. Stanley, <i>Symmetries of plane partitions</i>, J. Combin. Theory Ser. A <b>43</b> (1986), no. 1, 103–113.

[Ste1] J. R. Stembridge, <i>Some hidden relations involving the ten symmetry classes of plane partitions</i>, to appear in J. Combin. Theory Ser. A.

[Ste2] J. R. Stembridge, <i>A Maple package for root systems and finite Coxeter groups</i>, 1992, unpublished technical report.