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Finite quotients of singular Artin monoids and categorification of the desingularization map

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We study various aspects of the structure and representation theory of singular Artin monoids. This includes a number of generalizations of the desingularization map and explicit presentations for certain finite quotient monoids of diagrammatic nature. The main result is a categorification of the classical desingularization map for singular Artin monoids associated to finite Weyl groups using BGG category $\mathcal{O}$.

Abstract

We study various aspects of the structure and representation theory of singular Artin monoids. This includes a number of generalizations of the desingularization map and explicit presentations for certain finite quotient monoids of diagrammatic nature. The main result is a categorification of the classical desingularization map for singular Artin monoids associated to finite Weyl groups using BGG category $\mathcal{O}$.

참고문헌 (60)

  1. N. Antony, "On the injectivity of the Vassiliev homomorphism of singular Artin monoids", Bull. Austral. Math. Soc, 70(3), pp.401~422 (2004)[DOI]
  2. N. Antony, "On singular Artin monoids and contributions to Birman’s conjecture", Comm. Algebra, 33(11), pp.4043~4056 (2005)[DOI]
  3. E. Backelin, "The Hom-spaces between projective functors", Represent. Theory, 5, pp.267~283 (2001)[DOI]
  4. J. C. Baez, "Link invariants of finite type and perturbation theory", Lett. Math. Phys, 26(1), pp.43~51 (1992)[DOI]
  5. A. Beilinson, "Localisation de g-modules", C. R. Acad. Sci. Paris Ser. I Math, 292(1), pp.15~18 (1981)
  6. J. Bernstein, "Tensor products of finite- and infinite-dimensional representations of semisimple Lie algebras", Compositio Math, 41(2), pp.245~285 (1980)
  7. I. Bernstein, "Lie groups and their representations", pp.21~64 (1975), Halsted
  8. I. Bernstein, "A certain category of g-modules, (Russian)Funkcional", Anal. i Prilozen, 10(2), pp.1~8 (1976)
  9. S. Bigelow, "Braid groups and Iwahori-Hecke algebras, in Problems on mapping class groups and related topics", Proc. Sympos. Pure Math, pp.1090~ (2006)
  10. J. S. Birman, "New points of view in knot theory", Bull. Amer. Math. Soc. (N.S.), 28(2), pp.253~287 (1993)[DOI]
  11. R. Brauer, "On algebras which are connected with the semisimple continuous groups", Ann. of Math, 38(4), pp.857~872 (1937)[DOI]
  12. J.-L. Brylinski, "Kazhdan-Lusztig conjecture and holonomic systems", Invent. Math, 64(3), pp.387~410 (1981)
  13. K. J. Carlin, "Extensions of Verma modules", Trans. Amer. Math. Soc, 294(1), pp.29~43 (1986)[DOI]
  14. C.-W. Chen, "Extreme representations of semirings", Serdica Math. J, 44(3–4), pp.365~412 (2018)
  15. C. Clark, "Presentations for wreath products involving symmetric inverse monoids and categories", J. Algebra, 620, pp.630~668 (2023)
  16. A. Cohen, "Brauer algebras of type B", Forum Math, 27(2), pp.1163~1202 (2015)
  17. R. Corran, "A normal form for a class of monoids including the singular braid monoids", J. Algebra, 223(1), pp.256~282 (2000)[DOI]
  18. R. Corran, "Conjugacy in singular Artin monoids", J. Aust. Math. Soc, 79(2), pp.183~212 (2005)[DOI]
  19. K. Coulembier, "Dualities and derived equivalences for category O", Israel J. Math, 219(2), pp.661~706 (2017)
  20. D. Easdown, "Presentations of factorizable inverse monoids", Acta Sci. Math. (Szeged), 71(3–4), pp.509~520 (2005)
  21. J. East, "Birman’s conjecture is true for I2(p)", J. Knot Theory Ramifications, 15(2), pp.167~177 (2006)[DOI]
  22. J. East, "The factorizable braid monoid", Proc. Edinb. Math. Soc, 49(3), pp.609~636 (2006)[DOI]
  23. J. East, "Singular braids and partial permutations", Acta Sci. Math. (Szeged), 81(1-2), pp.55~77 (2015)[DOI]
  24. B. Everitt, "Partial mirror symmetry, lattice presentations and algebraic monoids", 107(2), pp.414~450 (2013)
  25. D. G. FitzGerald, "A presentation for the monoid of uniform block permutations", Bull. Austral. Math. Soc, 68(2), pp.317~324 (2003)[DOI]
  26. D. G. FitzGerald, "Dual symmetric inverse monoids and representation theory", J. Austral. Math. Soc. Ser. A, 64(3), pp.345~367 (1998)
  27. O. Ganyushkin, "Factor powers of semigroups of transformations", Dokl. Akad. Nauk Ukraini, 1993(12), pp.5~9 (1993)
  28. O. Ganyushkin, "Factor powers of finite symmetric groups", (Russian)Mat. Zametki, 58(2), pp.176~188 (1995)
  29. O. Ganyushkin, "The structure of subsemigroups of factor powers of finite symmetric groups", Mat. Zametki, 58(3), pp.341~354 (1995)
  30. O. Ganyushkin, "On the radical of FP+(Sn)", Mat. Stud, 20(1), pp.17~26 (2003)
  31. O. Ganyushkin, "Classical finite transformation semigroups: An introduction, Algebra and Applications" (2009), Springer-Verlag
  32. E. Godelle, "Geometric methods in group theory", pp.43~57 (2005), Amer. Math. Soc
  33. S. V. Hudzenko, "Automorphisms of a finitary factor power of an infinite symmetric group", Ukrainian Math. J, 62(7), pp.1158~1162 (2010)
  34. J. E. Humphreys, "Graduate Texts in Mathematics Vol. 9" (1972), Springer
  35. J. E. Humphreys, "Graduate Studies in Mathematics" (2008), Amer. Math. Soc
  36. Micha l Jab lonowski, "PRESENTATIONS AND REPRESENTATIONS OF SURFACE SINGULAR BRAID MONOIDS", 대한수학회지, 54(3), pp.749~762 (2017), 대한수학회
  37. D. Kazhdan, "Representations of Coxeter groups and Hecke algebras", Invent. Math, 53(2), pp.165~184 (1979)
  38. M. Khovanov, "Quivers, Floer cohomology, and braid group actions", J. Amer. Math. Soc, 15(1), pp.203~271 (2002)
  39. M. Kosuda, "Irreducible representations of the party algebra", Osaka J. Math, 43(2), pp.431~474 (2006)[DOI]
  40. G. Kudryavtseva, "On presentations of Brauer-type monoids", Cent. Eur. J. Math, 4(3), pp.413~434 (2006)
  41. P. Martin, "Temperley-Lieb algebras for nonplanar statistical mechanics—the partition algebra construction", J. Knot Theory Ramifications, 3(1), pp.51~82 (1994)[DOI]
  42. P. Martin, "Partitioned binary relations", Math. Scand, 113(1), pp.30~52 (2013)
  43. P. Martin, "On the representation theory of partial Brauer algebras", Q. J. Math, 65(1), pp.225~247 (2014)
  44. V. Mazorchuk, "On the structure of Brauer semigroup and its partial analogue", Problems in Algebra, 13, pp.29~45 (1998)
  45. V. Mazorchuk, "All automorphisms of FP+(Sn) are inner", Semigroup Forum, 60(3), pp.486~490 (2000)[DOI]
  46. V. Mazorchuk, "Some homological properties of the category O", Pacific J. Math, 232(2), pp.313~341 (2007)[DOI]
  47. V. Mazorchuk, "Applications of the category of linear complexes of tilting modules associated with the category O", Algebr. Represent. Theory, 12(6), pp.489~512 (2009)[DOI]
  48. V. Mazorchuk, "Simple modules over factorpowers", Acta Sci. Math. (Szeged), 75(3-4), pp.467~485 (2009)
  49. V. Mazorchuk, "Jucys-Murphy elements and Grothendieck groups for generalized rook monoids", J. Comb. Algebra, 6(1–2), pp.185~222 (2022)
  50. V. Mazorchuk, "Multiparameter colored partition category and the product of reduced Kronecker coefficients", ~
  51. V. Mazorchuk, "Double Catalan monoids", J. Algebraic Combin, 36(3), pp.333~354 (2012)
  52. V. Mazorchuk, "Translation and shuffling of projectively presentable modules and a categorification of a parabolic Hecke module", Tran. Amer. Math. Soc, 357(7), pp.2939~2973 (2005)
  53. V. Mazorchuk, "On functors associated to a simple root", J. Algebra, 314(1), pp.97~128 (2007)
  54. L. Paris, "The proof of Birman’s conjecture on singular braid monoids", Geom. Topol, 8, pp.1281~1300 (2004)[DOI]
  55. R. Plemmons, "On the semigroup of binary relations", Pacific J. Math, 35, pp.743~753 (1970)
  56. R. Rouquier, "Trends in representation theory of algebras and related topics", pp.137~167 (2006), Amer. Math. Soc
  57. W. Soergel, "Kategorie O, perverse Garben und Moduln ¨uber den Koinvarianten zur Weylgruppe", J. Amer. Math. Soc, 3(2), pp.421~445 (1990)[DOI]
  58. W. Soergel, "Kazhdan-Lusztig-Polynome und unzerlegbare Bimoduln uber Polynomringen", J. Inst. Math. Jussieu, 6(3), pp.501~525 (2007)[DOI]
  59. C. Stroppel, "Category O: gradings and translation functors", J. Algebra, 268(1), pp.301~326 (2003)[DOI]
  60. V. Vershinin, "On the singular braid monoid, St", Petersburg Math. J, 21(5), pp.19~36 (2010)[DOI]

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