Milen Yakimov - Publications

  1. Prime spectra of abelian 2-categories and categorifications of Richardson varieties (with Kent Vashaw) preprint, pdf, arXiv:1802.00488.
  2. Cluster algebra structures on Poisson nilpotent algebras (with K. R. Goodearl) preprint, pdf, arXiv:1801.01963.
  3. C-vectors of 2-Calabi-Yau categories and Borel subalgebras of sl (with Peter Jørgensen) preprint, pdf, arXiv:1710.06492.
  4. Twist invariants of graded algebras (with K. R. Goodearl) preprint, pdf, arXiv:1706.06957.
  5. The Poisson geometry of the 3-dimensional Sklyanin algebras (with Chelsea Walton and Xingting Wang) preprint, pdf, arXiv:1704.04975.
  6. Azumaya loci and discriminant ideals of PI algebras (with Ken A. Brown), preprint, pdf, arXiv:1702.04305.
  7. The Berenstein-Zelevinsky quantum cluster algebra conjecture (with K. R. Goodearl), preprint, pdf, ps, arXiv:1602.00498.
  8. Noncommutative discriminants via Poisson primes (with Bach Nguyen and Kurt Trampel), Adv. Math. 322 (2017), 269-307. pdf, ps, arXiv:1603.02585.
  9. Rigidity of quadratic Poisson tori (with Jesse Levitt), to appear in Bull. Inst. Math. Acad. Sinica (issue in honor of G. Lusztig's 70th birthday) pdf, arXiv:1609.06770.
  10. Quantized Weyl algebras at roots of unity (with Jesse Levitt), to appear in Israel J. Math., pdf, arXiv:1606.02121.
  11. Recovering the topology of surfaces from cluster algebras (with Eric Bucher), Math. Zeitschrift DOI: doi:10.1007/s00209-017-1901-4, pdf, arXiv:1607.02131.
  12. Prime factors of quantum Schubert cell algebras and clusters for quantum Richardson varieties (with T. H. Lenagan), Journal für die Reine und Angew. Math. DOI: 10.1515/crelle-2016-0046, pdf, ps, arXiv:1503.06297.
  13. Noncommutative bispectral Darboux transformations (with Joel Geiger and Emil Horozov), Trans. Amer. Math. Soc. 369 (2017), 5889-5919, pdf, ps, arXiv:1508.07879 .
  14. Quantum cluster algera structures on quantum nilpotent algebras (with K. R. Goodearl), Memoirs Amer. Math. Soc. 247 (2017), no. 1169, vii + 119pp., pdf, ps, arXiv:1309.7869.
  15. Separating Ore sets for prime ideals of quantum algebras (with Siân Fryer), Bull. London Math. Soc. 46 (2017), 202-215, pdf, ps, arXiv:1602.05052.
  16. From quantum Ore extensions to quantum tori via noncommutative UFDs (with K. R. Goodearl), Adv. Math. 300 (2016), 672-716, pdf, ps, arXiv:1208.6267.
  17. Unipotent and Nakayama automorphisms of quantum nilpotent algebras (with K. R. Goodearl), In: Commutative Algebra and Noncommutative Algebraic Geometry II: Research Articles, Eds: D. Eisenbud et al, pp 181-212, MSRI Publ. Vol 68. Cambridge Univ Press, 2015, pdf, ps, arXiv:1311.0278.
  18. Weak splittings of quotients of Drinfeld and Heisenberg doubles , In: Developments and retrospectives in Lie theory, geometric and analytic methods, Eds: G. Mason et al, pp. 245-268, Developments in Math 37, Springer 2014, pdf, ps, arXiv:1402.0883.
  19. Quantum cluster algebras and quantum nipotent algebras (with K. R. Goodearl), Proc. Natl. Acad. Sci. USA 111 (2014) no. 27, 9696-9703, pdf, ps, arXiv:1508.03086.
  20. Rigidity of quantum tori and the Andruskiewitsch-Dumas conjecture , Selecta Math. 20 (2014), no. 2, 421-464, pdf, ps, arXiv:1204.3218.
  21. On the spectra of quantum groups , Memoirs Amer. Math. Soc. 229 (2014), no. 1078, vi + 91pp., pdf, ps, arXiv:1106.3821.
  22. Quantum Schubert cells via representation theory and ring theory (with Joel Geiger), Michigan Math. J. 63, (2014), no. 1, 125-157. pdf, ps, arXiv:1203.3780.
  23. Spectra and catenarity of multiparameter quantum Schubert cells , Glasgow Math. J. 55A (2013), 169-194, (issue in honor of K. A. Brown's and J. T. Stafford's 60th birthdays), pdf, ps, arXiv:1112.2235.
  24. The Launois-Lenagan conjecture , J. Algebra 392 (2013), 1-9, pdf, ps, arXiv:1204.5440.
  25. Cominuscule parabolics of simple finite dimensional Lie superalgebras (with Dimitar Grantcharov), Jour. Pure Appl. Algebra 217 (2013), 1844-1863, pdf, ps, arXiv:1201.0199.
  26. A proof of the Goodearl-Lenagan polynormality conjecture , Int. Math. Res. Not. IMRN 2013, no. 9, 2097-2132, pdf, ps, arXiv:1109.3065.
  27. Strata of prime ideals of De Concini-Kac-Procesi algebras and Poisson geometry , In: New trends in noncommutative algebra (issue in honor of K. R. Goodearl's 65th birthday), eds: P. Ara et al., Contem. Math. 562, pp. 265-278, Amer. Math. Soc. 2012, pdf, ps, arXiv:1103.3451.
  28. Invariant prime ideals in quantizations of nilpotent Lie algebras , Proc. London Math. Soc. 101 (2010), 454-476, pdf, ps, arXiv:0905.0852.
  29. A classification of H-primes of quantum partial flag varieties , Proc. Amer. Math. Soc. 138 (2010), 1249-1261, pdf, ps, arXiv:0910.0997.
  30. Cyclicity of Lusztig's stratification of Grassmannians and Poisson geometry , In: Noncommutative structures in mathematics and physics, eds: S. Caenepeel et al., pp. 258-262, Royal Flemish Acad. of Belgium for Sciences and Arts, 2010, pdf, ps, arXiv:0902.2181.
  31. Completeness of determinantal Hamiltonian flows on the matrix affine Poisson space (with Michael Gekhtman), Lett. Math. Phys., 90 (2009), 161-173, pdf, ps, arXiv:0809.4650.
  32. Poisson structures on affine spaces and flag varieties. II. (with K. R. Goodearl), Trans. Amer. Math. Soc. 361 (2009), 5753-5780. pdf, ps. math.QA/0509075.
  33. 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.
  34. 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.
  35. 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.
  36. 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.
  37. Partitions of the wonderful group compactification (with Jiang-Hua Lu), Transformation Groups 12 (2007), no. 4, 695-723, pdf, ps, math.RT/0606579.
  38. Affine Jacquet functors and Harish-Chandra categories , Adv. Math. 208 (2007), 40-74. pdf ps, math.RT/0302269.
  39. 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.
  40. 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.
  41. 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.
  42. 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.
  43. Symplectic leaves of complex reductive Poisson-Lie groups , Duke Math. J. 112 (2002), 453-509, math.QA/00004102
  44. Quantum invariant measures (with Nicolai Reshetikhin) Comm. Math. Phys. 224 (2001), 399-426, math.QA/0101048
  45. Discrete Darboux transformations from Jacobi polynomials (with Alberto Grunbaum), Pacific J. Math. 204 395-432 (2002). math.CA/0012191
  46. The double and dual of a quasitriangular Lie bialgebra (with Tim Hodges), Math. Res. Lett. 8 (2001), 91-105, math.QA/0008086
  47. 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
  48. 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
  49. 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
  50. Highest weight modules over the W1+∞ algebra and the bispectral problem (with B. Bakalov and E. Horozov), Duke Math. J. 93 (1998), no. 1, 41-72, q-alg/9602012
  51. 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
  52. B\"acklund-Darboux transformations in Sato's Grassmannian (with B. Bakalov and E. Horozov), Serdica Math. J. 22 (1996) 571-586, q-alg/9602010
  53. 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
  54. Tau-functions as highest weight vectors for W1+∞ algebra (with B. Bakalov and E. Horozov), J. Phys. A 29 (1996), 5565-5573, hep-th/9510211