HENRY JACK
1917-1978
3
[15] (see also [14]. Henry left a considerable number of papers (including[13]),
notes and lecture material, much of which was almost ready for publication. This
material is deposited in the Dundee University Archives.
Like many young people of Henry Jack's generation World War II had a decisive
influence on future careers and aspirations. Had Henry had the opportunity to be
involved earlier with the type of problems in which his talents could find expression
then I am sure he would have made even greater contributions to analysis and group
representations (even possibly to multi-variate statistics) and due recognition would
have been accorded him during his lifetime.
Acknowledgements I am grateful to the Edinburgh Mathematical Society
and to the Royal Society of Edinburgh for granting permission to use extracts from
the obituary notices of A.D. Sands (Proc. Ed. Math. Soc (1979)) and W. N.
Everitt (Year Book of the Royal Society of Edinburgh (1979)). I am particularly
grateful to Dundee University who have generously allowed me access to Henry
Jack's unpublished papers and notes which were inspirational to the Workshop.
Indeed it provided the opportunity to rescue the important manuscript [13] which
is published for the first time in this volume.
References
[1] The volume of a certain set of matrices. Proc. Camb. Phil. Soc. 55, 1959, 213-223,(with A.
M. Macbeath)
[2] An application of the addition theorem for determinants. Proc. Edin. Math. Soc. 13, 1962,
165-166.
[3] An integral over the interior of a simplex. Proc. Edin. Math. Soc. 13, 1962, 167-171.
[4] A generalization of Dirichlet's multiple integral. Proc. Edin. Math. Soc. 14, 1965, 233-237.
[5] The gamma function without infinite products. Proc. Edin. Math. Soc. 14, 1965, 249-253.
[6] Jacobians of transformations involving orthogonal matrices. Proc. Roy. Soc. Edin. Sect. A.
67, 1966, 81-103.
[7] The asymptotic value of the volume of a certain set of matrices. Proc. Edin. Math. Soc. 15,
1967, 209-213.
[8] A matrix analogue of the integral
J:
x"'dx. Proc. Roy. Soc. Edin. Sect. A. 67, 1967, 205-214.
[9] On the integrals of Hua and James. Proc. Roy. Soc. Edin. Sect. A. 68, 1968, 54-69.
[10] A class of symmetric polynomials with a parameter. Proc. Roy. Soc. Edin. Sect. A. 69, 1970,
1-18.
[11] A surface integral and symmetric functions. Proc. Roy. Soc. Edin. Sect. A. 69, 1972, 347-364.
[12] A generalization of an early multivariate integral. Proc. Edin. Math. Soc. 18, 1972, 125-128.
[13] A class of polynomials in search of a definition, or the symmetric group parametrised, April
1976, Manuscript .This Volume
[14] I. G. Macdonald, Commentary on the previous paper, This volume.
[15]
R.
P. Stanley, Some combinatorial properties of Jack symmetric functions, Adv. in Math.
77,
1989, 76-115
School of Mathematics, University of Leeds, Leeds, LS2 9JT
E-mail address: bds@maths.leeds.ac. uk
CONTEMPORARY MATHEMATICS 5
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