Milen Yakimov - Publications

  1. Invariant prime ideals in quantizations of nilpotent Lie algebras , pdf, ps, arXiv:0905.0852.
  2. Cyclicity of Lusztig's stratification of Grassmannians and Poisson geometry pdf, ps, arXiv:0902.2181.
  3. Completeness of determinantal Hamiltonian flows on the matrix affine Poisson space (with Michael Gekhtman), pdf, ps, arXiv:0809.4650.
  4. The real loci of Calogero--Moser spaces, representations of rational Cherednik algebras and the Shapiro conjecture (with Iain Gordon and Emil Horozov), pdf, ps, arXiv:0711.4336.
  5. Modular classes of regular twisted Poisson structures on Lie algebroids (with Yvette Kosmann-Schwarzbach), Lett. Math. Phys. 80 (2007), 183-197, pdf, ps, math.SG/0701209.
  6. Group orbits and regular partitions of Poisson manifolds (with Jiang-Hua Lu), Comm. Math. Phys. 283 (2008), no. 3, 729-748, pdf, ps, math.SG/0609732.
  7. A Deodhar type stratification on the double flag variety (with Ben Webster), Transformation Groups 12 (2007), no. 4, 769--785, pdf, ps, math.SG/0607374.
  8. Partitions of the wonderful group compactification (with Jiang-Hua Lu), Transformation Groups 12 (2007), no. 4, 695--723, pdf, ps, math.RT/0606579.
  9. Spaces of flat G-connections over surfaces and symmetrically factorizable Poisson Lie groups (with Rinat Kashaev and Nicolai Reshetikhin), in preparation.
  10. Poisson structures on affine spaces and flag varieties. II. (with K. R. Goodearl), pdf, ps. math.QA/0509075, to appear in Trans. AMS.
  11. Poisson structures on affine spaces and flag varieties. I. Matrix affine Poisson space (with K. A. Brown and K. R. Goodearl), Adv. Math. 206 (2006), 567--629, pdf, ps. math.RT/0501109.
  12. On a class of double cosets in reductive algebraic groups (with Jiang-Hua Lu), pdf, ps, math.RT/0410006, Int. Math. Res. Notices 2005, no. 13, pp. 761-797.
  13. The prolate spheroidal phenomenon and bispectral algebras of ranks 1 and 2 (with Alberto Grunbaum), latest file pdf, ps.
  14. Triangular Poisson structures on Lie groups and symplectic reduction (with Tim Hodges), pdf, ps, math.SG/0412082, Noncommutative geometry and representation theory in mathematical physics, 123--134, Contemporary Mathematics 391.
  15. The prolate spheroidal phenomenon as a consequence of bispectrality (with Alberto Grunbaum), pdf, ps, math-ph/0303041 In: Workshop on Superintegrability, Eds. P. Tempesta and P. Winternitz, CRM Proceedings 37, Montreal, 2004, pp. 301-312.
  16. Affine Jacquet functors and Harish-Chandra categories , Adv. Math. 208 (2007), 40--74. pdf ps, math.RT/0302269.
  17. Categories of modules over an affine Kac-Moody algebra and finiteness of the Kazhdan-Lusztig tensor product , J. Algebra 319 (2008), no. 8, 3175--3196. pdf ps, math.RT/0210180.
  18. Symplectic leaves of complex reductive Poisson-Lie groups , Duke Math. J. 112 (2002), 453-509, math.QA/00004102
  19. Quantum invariant measures (with Nicolai Reshetikhin) Comm. Math. Phys. 224 (2001), 399-426, math.QA/0101048
  20. Discrete Darboux transformations from Jacobi polynomials (with Alberto Grunbaum), Pacific J. Math. 204 395-432 (2002). math.CA/0012191
  21. The double and dual of a quasitriangular Lie bialgebra (with Tim Hodges), Math. Res. Lett. 8 (2001), 91-105, math.QA/0008086
  22. Deformation quantization of Lagrangian fiber bundles (with Nicolai Reshetikhin), In: Conf\'erence Mosh\'e Flato 1999, vol. 2, 269-288, Kluwer Acad. Publ. 2000, math.QA/9907164
  23. Automorphisms of the Weyl algebra and bispectral operators (with B. Bakalov and E. Horozov), In: The bispectral problem, 3-10, CRM Proceedings, Montreal 1998, q-alg/9707018
  24. General methods for constructing bispectral operators (with B. Bakalov and E. Horozov), Phys. Lett. A. 222 (1996), no. 1-2, 59-66, q-alg/9605011
  25. Highest weight modules over the W_{1+infty} algebra and the bispectral problem (with B. Bakalov and E. Horozov), Duke Math. J. 93 (1998), no. 1, 41-72, q-alg/9602012
  26. Bispectral algebras of commuting ordinary differential operators (with B. Bakalov and E. Horozov), Comm. Math. Phys. 190 (1997), no. 2, 331-373, q-alg/9602011
  27. B\"acklund-Darboux transformations in Sato's Grassmannian (with B. Bakalov and E. Horozov), Serdica Math. J. 22 (1996) 571-586, q-alg/9602010
  28. Highest weight modules of W_{1+infty}, Darboux transformations and the bispectral problem (with B. Bakalov and E. Horozov), In: Conference on Geometry and Mathematical Physics (Bulgaria, 1995). Serdica Math. J. 23 (1997) 95--112, q-alg/9601017
  29. Tau-functions as highest weight vectors for W_{1+infty} algebra (with B. Bakalov and E. Horozov), J. Phys. A 29 (1996), 5565-5573, hep-th/9510211