Representation-theoretic proof of the inner product and symmetry identities for Macdonald's polynomials
Pavel I. Etingof, Alexander A. Kirillov, Jr. (1996)
Compositio Mathematica
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Displaying similar documents to “Algebraic integrability of Schrodinger operators and representations of Lie algebras”
Representation-theoretic proof of the inner product and symmetry identities for Macdonald's polynomials
Super boson-fermion correspondence
Victor G. Kac, J. W. Van de Leur (1987)
Annales de l'institut Fourier
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We establish a super boson-fermion correspondence, generalizing the classical boson-fermion correspondence in 2-dimensional quantum field theory. A new feature of the theory is the essential non-commutativity of bosonic fields. The superbosonic fields obtained by the super bosonization procedure from super fermionic fields form the affine superalgebra . The converse, super fermionization procedure, requires introduction of the super vertex operators. As applications, we give vertex...
Harmonic analysis on quantum spheres associated with representations of and -jacobi polynomials
Tetsuya Sugitani (1995)
Compositio Mathematica
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A trace formula for semi-simple Lie algebras
M. D. Gould (1980)
Annales de l'I.H.P. Physique théorique
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On characteristic identities for Lie algebras
D. M. O'Brien, A. Cant, A. L. Carey (1977)
Annales de l'I.H.P. Physique théorique
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Quantum integrable systems
Michael Semenov-Tian-Shansky (1993-1994)
Séminaire Bourbaki
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Calogero-Moser spaces and an adelic -algebra
Emil Horozov (2005)
Annales de l’institut Fourier
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We introduce a Lie algebra, which we call adelic -algebra. Then we construct a natural bosonic representation and show that the points of the Calogero-Moser spaces are in 1:1 correspondence with the tau-functions in this representation.