Milen Yakimov - Publications

  1. Root of unity quantum cluster algebras and discriminants (with Bach Nguyen and Kurt Trampel) preprint, pdf, arXiv:arXiv:2012.02314.
  2. Poisson orders on large quantum groups (with Nicolás Andruskiewitsch and Iván Angiono) preprint, pdf, arXiv:2008.11025.
  3. Noncommutative tensor triangular geometry and the tensor product property for support maps (with Daniel K. Nakano and Kent B. Vashaw) preprint, pdf, arXiv:2008.09924.
  4. Reflective prolate-spheroidal operators and the adelic Grassmannian (with W. Riley Casper, F. Alberto Grünbaum, and Ignacio Zurrián), preprint, pdf, arXiv:2003.11616.
  5. Bivariate continuous q-Hermite polynomials and deformed quantum Serre relations (with W. Riley Casper and Stefan Kolb) preprint, pdf, arXiv:2002.07895.
  6. Green groupoids of 2-Calabi-Yau categories, derived Picard actions, and hyperplane arrangements (with Peter Jørgensen) preprint, pdf, arXiv:1910.05560.
  7. Noncommutative tensor triangular geometry (with Daniel K. Nakano and Kent B. Vashaw) preprint, pdf, arXiv:1909.04304.
  8. Integral quantum cluster structures (with K. R. Goodearl) preprint, pdf, arXiv:2003.04434.
  9. The matrix Bochner problem (with W. Riley Casper) preprint, pdf, arXiv:1803.04405.
  10. Poisson geometry and representations of PI 4-dimensional Sklyanin algebras (with Chelsea Walton and Xingting Wang) preprint, pdf, arXiv:1802.06487.
  11. Cluster algebra structures on Poisson nilpotent algebras (with K. R. Goodearl) preprint, pdf, arXiv:1801.01963.
  12. Integral operators, bispectrality and growth of Fourier algebras (with W. Riley Casper), J. Reine Angew. Math. doi: 10.1515/crelle-2019-0031, pdf, arXiv:1807.09314.
  13. The Berenstein-Zelevinsky quantum cluster algebra conjecture (with K. R. Goodearl), J. Eur. Math. Soc. (JEMS) 22 (2020), no. 8, 2453-2509. pdf, ps, arXiv:1602.00498.
  14. Symmetric pairs for Nichols algebras of diagonal type via star products (with Stefan Kolb), Adv. Math. 365 (2020), 107042, 69pp., pdf, arXiv:1901.00490.
  15. C-vectors of 2-Calabi-Yau categories and Borel subalgebras of sl (with Peter Jørgensen), Selecta Math. (N.S.) 26 (2020), no. 1, Art. 1, 46 pp., pdf, arXiv:1710.06492.
  16. Reflective prolate-spheroidal operators and the KP/KdV equations (with W. Riley Casper, F. Alberto Grünbaum, and Ignacio Zurrián), Proc. Natl. Acad. Sci. USA 116 (2019), no. 37, 18310-18315, pdf, arXiv:1909.01448.
  17. Prime spectra of abelian 2-categories and categorifications of Richardson varieties (with Kent Vashaw), in "Representations and Nilpotent Orbits of Lie Algebraic Systems, in honour of the 75th birthday of Tony Joseph", Progr. in Math. vol. 330, eds. M. Gorelik et al, pp. 501-553, Birkhäuser, 2019. pdf, arXiv:1802.00488.
  18. Poisson geometry of PI 3-dimensional Sklyanin algebras (with Chelsea Walton and Xingting Wang), Proc. London Math Soc. 118 (2019), 1471-1500, pdf, arXiv:1704.04975.
  19. Prime factors of quantum Schubert cell algebras and clusters for quantum Richardson varieties (with T. H. Lenagan), J. Reine Angew. Math. 750 (2019), 123-156, pdf, ps, arXiv:1503.06297.
  20. Azumaya loci and discriminant ideals of PI algebras (with Ken A. Brown), Adv. Math. 340 (2018), 1219-1255, pdf, arXiv:1702.04305.
  21. Quantized Weyl algebras at roots of unity (with Jesse Levitt), Israel J. Math. 225 (2018), 681-719, pdf, arXiv:1606.02121.
  22. Recovering the topology of surfaces from cluster algebras (with Eric Bucher), Math. Zeitschrift 288 (2018), 565-594, pdf, arXiv:1607.02131.
  23. Rigidity of quadratic Poisson tori (with Jesse Levitt), Bull. Inst. Math. Acad. Sinica 13 (2018), 99-142 (issue in honor of G. Lusztig's 70th birthday) pdf, arXiv:1609.06770.
  24. Twist invariants of graded algebras (with K. R. Goodearl) in: Advances in Rings and Modules (volume in honor of B. Muller), Contemp. Math. 715 (2018), pp. 141-170. pdf, arXiv:1706.06957.
  25. Noncommutative discriminants via Poisson primes (with Bach Nguyen and Kurt Trampel), Adv. Math. 322 (2017), 269-307. pdf, ps, arXiv:1603.02585.
  26. Noncommutative bispectral Darboux transformations (with Joel Geiger and Emil Horozov), Trans. Amer. Math. Soc. 369 (2017), 5889-5919, pdf, ps, arXiv:1508.07879 .
  27. 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.
  28. 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.
  29. 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.
  30. 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.
  31. 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.
  32. 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.
  33. Rigidity of quantum tori and the Andruskiewitsch-Dumas conjecture , Selecta Math. (N.S.) 20 (2014), no. 2, 421-464, pdf, ps, arXiv:1204.3218.
  34. On the spectra of quantum groups , Memoirs Amer. Math. Soc. 229 (2014), no. 1078, vi + 91pp., pdf, ps, arXiv:1106.3821.
  35. 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.
  36. 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.
  37. The Launois-Lenagan conjecture , J. Algebra 392 (2013), 1-9, pdf, ps, arXiv:1204.5440.
  38. Cominuscule parabolics of simple finite dimensional Lie superalgebras (with Dimitar Grantcharov), Jour. Pure Appl. Algebra 217 (2013), 1844-1863, pdf, ps, arXiv:1201.0199.
  39. A proof of the Goodearl-Lenagan polynormality conjecture , Int. Math. Res. Not. IMRN 2013, no. 9, 2097-2132, pdf, ps, arXiv:1109.3065.
  40. 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.
  41. Invariant prime ideals in quantizations of nilpotent Lie algebras , Proc. London Math. Soc. 101 (2010), 454-476, pdf, ps, arXiv:0905.0852.
  42. A classification of H-primes of quantum partial flag varieties , Proc. Amer. Math. Soc. 138 (2010), 1249-1261, pdf, ps, arXiv:0910.0997.
  43. 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.
  44. 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.
  45. 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.
  46. 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.
  47. 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.
  48. 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.
  49. 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.
  50. Partitions of the wonderful group compactification (with Jiang-Hua Lu), Transformation Groups 12 (2007), no. 4, 695-723, pdf, ps, math.RT/0606579.
  51. Affine Jacquet functors and Harish-Chandra categories , Adv. Math. 208 (2007), 40-74. pdf ps, math.RT/0302269.
  52. 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.
  53. 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.
  54. 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.
  55. 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.
  56. Symplectic leaves of complex reductive Poisson-Lie groups , Duke Math. J. 112 (2002), 453-509, math.QA/00004102
  57. Quantum invariant measures (with Nicolai Reshetikhin) Comm. Math. Phys. 224 (2001), 399-426, math.QA/0101048
  58. Discrete Darboux transformations from Jacobi polynomials (with Alberto Grunbaum), Pacific J. Math. 204 395-432 (2002). math.CA/0012191
  59. The double and dual of a quasitriangular Lie bialgebra (with Tim Hodges), Math. Res. Lett. 8 (2001), 91-105, math.QA/0008086
  60. 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
  61. 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
  62. 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
  63. 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
  64. 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
  65. B\"acklund-Darboux transformations in Sato's Grassmannian (with B. Bakalov and E. Horozov), Serdica Math. J. 22 (1996) 571-586, q-alg/9602010
  66. 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
  67. 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