Doug Pickrell: Publications, and some preprints.

  1. Notes on invariant measures for loop groups, arXiv:2207.09913
  2. (with Mohammad Latifi) Conversations with Flaschka, Kac-Moody Groups and Verblunsky coefficients, Physics D (2023)
  3. A question about total positivity and Newman's Fourier transforms with real zeroes, ArXiv 2104.05143
  4. (with Estelle Basor) Loops in SU(2,C) and factorization, II, in Toeplitz Operators and Random Matrices (in memory of Harold Widom), Birkhauser (2022). A long version in ArXiv 2009.14267
  5. (with Mohammad Latifi) Exponential of the S^1 trace of the free field and Verblunsky coefficients, Rocky Mountain Journal of Mathematics (2022), https://arxiv.org/abs/2002.06455
  6. (with Andres Larrain-Hubach) Sobolev mapping groups and curvature, Letters Math Physics 109 (5), (2019), 1257-1267.
  7. Complex groups and factorization, J. Lie Theory 28, no. 4 (2018) 1095-1118, ArXiv 1707.07758
  8. (with Estelle Basor) Loops in SL(2,C) and factorization, Random Matrices: Theory and Applications, Vol. 7, No. 3 (2018), 26 pp, ArXiv 1707.01437
  9. Solving for root subgroup coordinates: the SU(2) case, ArXiv 1509.05947 <\li>
  10. (with Estelle Basor) Loops in SU(2), Riemann surfaces, and factorization, SIGMA Symmetry Integrability Geom. Methods Anal. Volume in honor of P. Deift and C. Tracy (2016) ArXiv 1504.00715
  11. Open strings in compact Lie groups and factorization, in preparation
  12. Factorization of the invariant measure for Loops in SU(2), in preparation
  13. Representation varieties and symmetric spaces, in preparation
  14. P(\phi)_2 QFTs and Segal's axioms, II: critical limits, in preparation
  15. (with Arlo Caine) Non-compact groups of Hermitian symmetric type and factorization, Transformation Groups, Volume 22, Issue 1 (2017) 105-125, ArXiv 1503.08461
  16. (with Arlo Caine) Loops in noncompact groups and factorization, Generalized Lie Theory and Applications, Vol. 9, no. 2 (2015), 14 pp, ArXiv 1501.00917
  17. (with Patrick Nabelek) Harmonic maps and the symplectic category, ArXiv 1404.2899.
  18. (with Mark Dalthorp) Homeomorphisms of S^1 and factorization, IMRN (2019), https://academic.oup.com/imrn/advance-article/doi/10.1093/imrn/rnz297/5644428?guestAccessKey=95f2f131-b931-40aa-8858-ec39da82759a ArXiv 1408.5402
  19. (with Angel Chavez) Werner's measure on self-avoiding loops on Riemann surfaces and welding, SIGMA Symmetry Integrability Geom. Methods Anal. 10 (2014), 081, 42 pages; arXiv:1401.2675
  20. Loops in SU(2) and factorization, J.Funct. Anal. 260 (2011) 2191-2221, arXiv:0903.4983
  21. (with Benjamin Pittman-Polletta) Unitary loop groups and factorization, J. Lie Theory, Vol. 20 (2010) 93-112, arXiv 0905.2911
  22. Consistency of regularization for scalar free fields, Letters in Math. Phys., Vol 87, Issue 3 (2009) 283-290, ArXiv:0812.0107.
  23. Homogeneous Poisson structures on loop spaces of symmetric spaces, SIGMA 4 (2008), 069, arXiv:0801.3277, http://www.emis.de/journals/SIGMA/
  24. (with Arlo Caine) Homogeneous Poisson structures on symmetric spaces, IMRN, doi 10.1093/imrn/rnn 126 (2008) arXiv:0710.4484
  25. 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
  26. P(\phi)_2 quantum field theories and Segal's axioms, Comm. Math. Phys. 280 (2008) 403-425, math-ph/070207
  27. A survey of conformally invariant measures on H^m(\Delta), math.PR/0702672
  28. Heat kernel measures and regular representations of loop groups, in Infinite Dimensional Lie Theory, Oberwolfach Report no. 55 (2006)
  29. The diagonal distribution of the invariant measure for a compact symmetric space, Transformation Groups, Vol. 11, No. 4 (2006) 705-724 math.SG/0506283
  30. 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
  31. 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.
  32. "H^4(BK,Z) and operator algebras," J. Lie Theory, Vol 14 (2004) 199-213 .
  33. (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.
  34. (with Eugene Xia) Ergodicity of mapping class group actions on representation varieties, II. Surfaces with boundary, Transformation Groups 8, no 4 (2003) 397-402.
  35. (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.
  36. (with Eugene Xia) Ergodicity of mapping class group actions on representation varieties, I. Closed surfaces, Comment Math Helv 77 (2002) 339-362.
  37. (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.
  38. Extensions of loop groups, H^4(BK,Z), and reciprocity, preprint
  39. 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.
  40. Invariant measures for unitary groups associated to Kac-Moody Lie algebras, Memoirs of the AMS, Vol 146, No 693 (July 2000).
  41. YM_2 measures and area-preserving diffeomorphisms, J Geom and Physics 19, no 4 (1996) 315-367.
  42. Extensions of loop groups, in The Mathematical Legacy of Hanno Rund, Hadronic Press (1993) 87-134.
  43. Mackey analysis of infinite classical motion groups, Pac J Math 150, no 1 (1991) 139-166.
  44. Separable representations of automorphism groups of infinite rank symmetric spaces, J Funct Anal 90, no 1 (1990) 1-26.
  45. Harmonic analysis on infinite dimensional symmetric spaces, preprint

    46. 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].

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