R. Merris and J. A. Dias da Silva, Generalized Schur functions, J. Algebra 35 (1975), 442-448. Math Reviews 53#2979.


Extending an idea from [R. Merris and M. Newman, An explicit isomorphism with applications to inequalities for matrix functions, J. Algebra 25 (1973), 468-474], the authors explore generalized matrix functions based on arbitrary complex valued functions of the symmetric group. (Extensions of a different sort can be found in [M. Ishaq and R. Merris, Matrix functions afforded by entries of unitary representations, Linear Algebra Appl. 25 (1979), 255-269].) Subsequent work in this area is summarized in [R. Merris, Multilinear Algebra, Gordon & Breach, Amsterdam, 1997, pp 213-223]. Among the publications citing this article are

  • M. Marcus, Finite Dimensional Multilinear Algebra Part II, Marcel Dekker, NY, 1975.
  • E. H. Lieb, Advances in Math. 20 (1976), 174-178.
  • J. A. Dias da Silva, Linear & Multilinear Algebra 7 (1979), 343-357.
  • G. N. de Oliveira and J. A. Dias da Silva, Linear Algebra Appl. 28 (1979), 161-176.
  • J. A. Dias da Silva, Portugaliae Math. 39 (1980), 441-453.
  • J. A. Dias da Silva, Linear Algebra Appl. 40 (1981), 161-182.
  • J. A. Dias da Silva and Ma. da Purificacao Coelho, Linear Algebra Appl. 94 (1987), 165-179.
  • C. F. Chan, Linear & Multilinear Algebra 27 (1990), 189-198.
  • J. A. Dias da Silva and Ma. da Purificacao Coelho, Linear Algebra Appl. 140 (1990), 1-11.
  • C. F. Chan, Linear & Multilinear Algebra 34 (1993), 247-259.
  • E. A. Carlen and E. H. Lieb, Communications in Mathematical Physics 155 (1993), 27-46.
  • T. Pate, Linear Algebra Appl. 212/213 (1994), 31-44.
  • T. Pate, Linear & Multilinear Algebra 38 (1995), 295-302.
  • C. F. Chan, Linear Algebra Appl. 239 (1996), 15-27.
  • T. Lei, Acta Mathematica Sinica (Chinese) 39 (1996), 488-494.
  • T. Pate, Linear Algebra Appl. 254 (1997), 427-466.
  • T. Lei, Chinese Science Bull. 42 (1997), 22-26.
  • T. Pate, Linear Algebra Appl. 255 (1997), 203-242.
  • M.-P. Gong, Linear Algebra Appl. 257 (1997), 65-75.
  • T.-G. Lei, Linear Algebra Appl. 263 (1997), 311-332.
  • R. Bhatia, Matrix Analysis, Springer-Verlag, 1997.
  • E. A. Carlin and P. Kree, J. Functional Anal. 158 (1998), 475-508.