Doug Pickrell: Publications, and some preprints.

  1. Loops in SU(2) and factorization, J.Funct. Anal. 260 (2011) 2191-2221, arXiv:0903.4983
  2. (with Benjamin Pittman-Polletta) Unitary loop groups and factorization, J. Lie Theory, Vol. 20 (2010) 93-112, arXiv 0905.2911
  3. Consistency of regularization for scalar free fields, Letters in Math. Phys., Vol 87, Issue 3 (2009) 283-290, ArXiv:0812.0107.
  4. Homogeneous Poisson structures on loop spaces of symmetric spaces, SIGMA 4 (2008), 069, arXiv:0801.3277, http://www.emis.de/journals/SIGMA/
  5. (with Arlo Caine) Homogeneous Poisson structures on symmetric spaces, IMRN, doi 10.1093/imrn/rnn 126 (2008) arXiv:0710.4484
  6. Heat kernels and critical limits, Perspectives on Infinite Dimensional Lie Theory, edited by K-H Neeb and A. Pianzola, Progress in Mathematics 288, Birkhauser (2010) arXiv:0711.0410
  7. P(\phi)_2 quantum field theories and Segal's axioms, Comm. Math. Phys. 280 (2008) 403-425, math-ph/070207
  8. A survey of conformally invariant measures on H^m(\Delta), math.PR/0702672
  9. Heat kernel measures and regular representations of loop groups, in Infinite Dimensional Lie Theory, Oberwolfach Report no. 55 (2006)
  10. The diagonal distribution of the invariant measure for a compact symmetric space, Transformation Groups, Vol. 11, No. 4 (2006) 705-724 math.SG/0506283
  11. An invariant measure for the loop space of a compact simply connected symmetric space, J Funct Anal 234 (2006) 321-363, ArXiv math-ph/0409013
  12. The radial part of the zero-mode Hamiltonian for sigma models with group target space, Rev Math Physics, Vol 16, No 5 (June 2004) 603-628.
  13. "H^4(BK,Z) and operator algebras," J. Lie Theory, Vol 14 (2004) 199-213 .
  14. (with Jialing Dai) Coadjoint orbits for the Virasoro extension of Diff(S^1) and their representatives, Acta Math. Sci. Ser B Engl. Ed. 24 (2004) 185-205.
  15. (with Eugene Xia) Ergodicity of mapping class group actions on representation varieties, II. Surfaces with boundary, Transformation Groups 8, no 4 (2003) 397-402.
  16. (with Jialing Dai) The orbit method and the Virasoro extension  of Diff(S^1), I. Orbital integrals, J Geom and Physics 44 (2003) 623-653.
  17. (with Eugene Xia) Ergodicity of mapping class group actions on representation varieties, I. Closed surfaces, Comment Math Helv 77 (2002) 339-362.
  18. (with Karl-Hermann Neeb) Supplements to the papers entitled ``On a theorem of S. Banach'' [J. Lie Th 7, no 2 (1997) 293-300] by Neeb and ``The separable representations of  U(H) [Proc AMS 102, no 2 (1988) 416-420] by Pickrell, J. Lie Th, no. 1 (2000) 107-109.
  19. Extensions of loop groups, H^4(BK,Z), and reciprocity, preprint

    20. Abstract: Given a compact Lie group K, we classify the Aut(P)-invariant central extensions of the gauge group K(P), for each K-bundle P\toS^1. Given a level l\inH^4(BK,Z), we associate a central extension to each K(P) such that this family of extensions has a reciprocity property introduced by G Segal [Note: This paper is 15 years in development, and over 100 pages. It is a step in a larger project to address a conjecture of physicists, e.g. Moore and Seiberg, concerning the classification of rational conformal field theories]

  20. On the action of the group of diffeomorphisms of a surface on sections of the determinant line bundle, Pac J Math, Vol 193, No 1 (2000) 177-199.
  21. Invariant measures for unitary groups associated to Kac-Moody Lie algebras, Memoirs of the AMS, Vol 146, No 693 (July 2000).
  22. YM_2 measures and area-preserving diffeomorphisms, J Geom and Physics 19, no 4 (1996) 315-367.
  23. Extensions of loop groups, in The Mathematical Legacy of Hanno Rund, Hadronic Press (1993) 87-134.
  24. Mackey analysis of infinite classical motion groups, Pac J Math 150, no 1 (1991) 139-166.
  25. Separable representations of automorphism groups of infinite rank symmetric spaces, J Funct Anal 90, no 1 (1990) 1-26.
  26. Harmonic analysis on infinite dimensional symmetric spaces, preprint

    27. Abstract: In this paper we introduce a framework for harmonic analysis associated to infinite dimensional Riemannian symmetric spaces of classical type, involving the notion of a rigged manifold. We prove the existence (and in some cases uniqueness) of invariant measures associated to riggings of infinite dimensional classical symmetric spaces. The associated L^2 representations decompose uniquely as direct integrals of irreducible spherical representations [The Plancherel formula has been found by Borodin and Olshanskii].

  27. On the metric geometry of Schubert varieties, preprint.
  28. Separable representations of U(H), Proc AMS 102, no 2 (1988) 416-420.
  29. Decomposition of regular representations of U(H), Pac J Math 128, No2 (1987) 319-332.
  30. On the support of quasi-invariant measures on infinite dimensional Grassmann manifolds, Proc AMS 100, No 1 (1987) 111-116.
  31. Measures on infinite dimensional Grassmann manifolds, J Funct Anal 70, no 2 (1987) 323-356.