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Proctor, Robert A.

Shifted plane partitions of trapezoidal shape. (English) Zbl 0525.05007

Proc. Am. Math. Soc. 89, 553-559 (1983).
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Cited in 1 Review
Cited in 33 Documents

MathOverflow Questions:

Bender-Knuth involutions for symplectic (King) tableaux

MSC:

05A15 Exact enumeration problems, generating functions
20C30 Representations of finite symmetric groups
17B99 Lie algebras and Lie superalgebras

Keywords:

symplectic Lie algebras; plane partitions; shifted plane partitions; shifted shape
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References:

[1] Kenneth Baclawski, Character generators for unitary and symplectic groups, J. Math. Phys. 24 (1983), no. 7, 1688 – 1694. · Zbl 0518.22014 · doi:10.1063/1.525912
[2] H. Boerner, Representations of groups, North-Holland, London, 1969. · Zbl 0112.26301
[3] L. Carlitz, Rectangular arrays and plane partitions, Acta Arith. 13 (1967/1968), 29 – 47. · Zbl 0168.01502
[4] Paul H. Edelman, Zeta polynomials and the Möbius function, European J. Combin. 1 (1980), no. 4, 335 – 340. · Zbl 0451.06005 · doi:10.1016/S0195-6698(80)80034-5
[5] I. Gessel, Determinants and plane partitions, European J. Combin. (to appear).
[6] R. C. King, Branching rules for classical Lie groups using tensor and spinor methods, J. Phys. A 8 (1975), 429 – 449. · Zbl 0301.20029
[7] R. C. King, Weight multiplicities for the classical groups, Group theoretical methods in physics (Fourth Internat. Colloq., Nijmegen, 1975) Springer, Berlin, 1976, pp. 490 – 499. Lecture Notes in Phys., Vol. 50.
[8] I. G. Macdonald, Symmetric functions and Hall polynomials, The Clarendon Press, Oxford University Press, New York, 1979. Oxford Mathematical Monographs. · Zbl 0487.20007
[9] Robert A. Proctor, Bruhat lattices, plane partition generating functions, and minuscule representations, European J. Combin. 5 (1984), no. 4, 331 – 350. · Zbl 0562.05003 · doi:10.1016/S0195-6698(84)80037-2
[10] Richard P. Stanley, On the number of reduced decompositions of elements of Coxeter groups, European J. Combin. 5 (1984), no. 4, 359 – 372. · Zbl 0587.20002 · doi:10.1016/S0195-6698(84)80039-6
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