(GLn, GLm)-duality and symmetric plethysm

Roger Howe1
1The Institute for Advanced Studies, Hebrew University of Jerusalem, Jerusalem, Israel

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Chen Y, Garsia A and Remmel J, Algorithms for plethysm in combinatorics and algebra,Contemp. Math. AMS Providence RI 34 (1984) 109–153

Curtis C and Reiner I,Representation theory of finite groups and associative algebras (New York: Wiley-Interscience) (1962)

Duncan D, On D E Littlewood’s algebra of S-functions,Can. J. Math. 4 (1952) 504–512

Foulkes H, Concomitants of the quintic and sextic up to degree four in coefficients of the ground form.J. London Math. Soc. 25 (1950) 205–209

Gross K and Kunze R, Bessel functions and representation theory II. Holomorphic discrete series and metaplectic representations,J. Funct. Anal. 25 (1977) 1–49

Guillemin V. and Sternberg S,The Frobenius reciprocity theorems from a symplectic point of view in Nonlinear partial differential operators and quantization procedures, Lecture notes in math. No. 1037 (New York: Springer-Verlag) 1983, pp. 212–256

Howe R, The classical groups and invariants of binary forms in:Proceedings of the Hermann Weyl Centennial Symposium (Durham: AMS Publication) (1987) (to appear)

Howe R, Remarks on classical invariant theory (preprint)

Howe R, Transcending classical invariant theory (preprint)

Howe R, Reciprocity laws in the theory of dual pairs, in:Representation theory of reductive groups, Progress in mathematics (ed.) P Trombi (Boston: Birkhauser) vol 40 (1983) pp. 159–175

Howe R, Asymptotic dimensions of spaces of invariants (in preparation)

Jacobson N,Lie algebras (New York: Interscience Publishers) 1962

James G D, The representation theory of the symmetric groups,Lecture notes in mathematics, No. 682 (New York: Springer-Verlag) (1978)

Kashiwara M and Vergne M, On the Segal-Shale-Weil representations and harmonic polynomials,Invent. Math. 44 (1978) 1–47

Kempe A, On regular difference terms,Proc. London Math. Soc. 25 (1894) 465–470

Klink W and Ton-That T, Calculation of Clebsch-Gordan and Racah coefficients using symbolic manipulation programs (preprint)

Kung J and Rota G-C, The invariant theory of binary forms,BAMS (new series) 10 (1984) 27–85

Lang S,Algebra (Reading: Addison-Wesley) (1984)

Littelman P, A decomposition formula for Levi sub-groups (preprint)

Littlewood D,The theory of group characters and matrix representations of groups (Oxford: University Press) (1940)

MacDonald I,Symmetric functions and Hall polynomials (Oxford: University Press) (1979)

Stanley R, GLn(ℂ) for combinatorialists, in:Surveys in combinatorics (ed.) E K Lloyd (Cambridge: University Press) London Math. Soc. Lecture Notes No. 82 (1983)

Thrall R, On symmetrized Kronecker powers and the structure of the free Lie ring,Am. J. Math. 64 (1942) 371–388

Weyl H,The classical groups (Princeton: University Press) (1946)

Zhelobenko D, Compact Lie groups and their representations, Trans. Math. Mono. No. 40, AMS Providence (1973)