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Jack's unpublished papers and notes which were inspirational to the Workshop.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