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The classification results for the extreme characters of two basic "big" groups, the infinite symmetric group S(infinity) and the infinite-dimensional unitary group U(infinity), are remarkably similar.
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1983
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D. Pickrell, Measures on infinite dimensional Grassmann manifold
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A. M. Vershik and S. V. Kerov, The Grothendieck group of infinite symmetric group and symmetric functions (with the elements of the theory of K 0 K_{0} -functor for AF-algebas)
1990
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S. Kerov, G. Olshanski, and A. Vershik, Harmonic analysis on the infinite symmetric group. A deformation of the regular representation
1993
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Yu. A. Neretin, Hua-type integrals over unitary groups and over projective limits of unitary groups
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2003
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2003
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G. Olshanski, The problem of harmonic analysis on the infinite-dimensional unitary group
2003
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1994
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I. G. Macdonald, Symmetric Functions and Hall Polynomials
1995
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A. V. Gnedin, The representation of composition structures
1997
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H. Weyl, The classical groups. Their invariants and representations
1997
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S. Kerov, A. Okounkov, and G. Olshanski, The boundary of Young graph with Jack edge multiplicities
1998
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A. Okounkov and G. Olshanski, Shifted Schur functions
1998
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A. Okounkov and G. Olshanski, Asymptotics of Jack polynomials as the number of variables goes to infinity
1998
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G. Olshanski, A. Regev, and A. Vershik, Frobenius-Schur functions
2003
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S. Kerov, G. Olshanski, and A. Vershik, Harmonic analysis on the infinite symmetric group
2004
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A. Borodin and G. Olshanski, Harmonic analysis on the infinite-dimensional unitary group and determinantal point processes
2005
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A. Borodin and G. Olshanski, Representation theory and random point processes
2005
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A. Borodin and G. Olshanski, Markov processes on partitions
2006
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A. Gnedin and G. Olshanski, Coherent permutations with descent statistic and the boundary problem for the graph of zigzag diagrams
2006
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A. Borodin and G. Olshanski, Infinite-dimensional diffusions as limits of random walks on partitions
2009
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2010
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2029
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