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Volumn 12, Issue 3-4, 2007, Pages 379-431

A categorification of finite-dimensional irreducible representations of quantum sl2 and their tensor products

Author keywords

Canonical bases; Categorification; Flag varieties; Lie algebras; Quantum groups

Indexed keywords


EID: 34047261097     PISSN: 10221824     EISSN: 14209020     Source Type: Journal    
DOI: 10.1007/s00029-007-0031-y     Document Type: Article
Times cited : (81)

References (51)
  • 1
    • 0001768267 scopus 로고
    • Representations of quantum groups at a pth root of unity and of semisimple groups in characteristic p: Independence of p
    • H. H. Andersen, J. C. Jantzen, and W. Soergel. Representations of quantum groups at a pth root of unity and of semisimple groups in characteristic p: independence of p. Astérisque. 220 (1994).
    • (1994) Astérisque , vol.220
    • Andersen, H.H.1    Jantzen, J.C.2    Soergel, W.3
  • 5
    • 0030528385 scopus 로고    scopus 로고
    • Koszul duality patterns in representation theory
    • A. Beilinson, V. Ginzburg, and W. Soergel. Koszul duality patterns in representation theory. J. Amer. Math. Soc. 9 (1996), 473-527.
    • (1996) J. Amer. Math. Soc , vol.9 , pp. 473-527
    • Beilinson, A.1    Ginzburg, V.2    Soergel, W.3
  • 8
    • 0000588626 scopus 로고
    • Tensor products of finite- and infinite-dimensional representations of semisimple Lie algebras
    • J. N. Bernstein and S. I. Gel'fand. Tensor products of finite- and infinite-dimensional representations of semisimple Lie algebras. Compos. Math. 41 (1980), 245-285.
    • (1980) Compos. Math , vol.41 , pp. 245-285
    • Bernstein, J.N.1    Gel'fand, S.I.2
  • 9
    • 0002570278 scopus 로고
    • Differential operators on homogeneous spaces. III. Characteristic varieties of Harish-Chandra modules and of primitive ideals
    • W. Borho and J.-L. Brylinski. Differential operators on homogeneous spaces. III. Characteristic varieties of Harish-Chandra modules and of primitive ideals. Invent. Math. 80 (1985), 1-68.
    • (1985) Invent. Math , vol.80 , pp. 1-68
    • Borho, W.1    Brylinski, J.-L.2
  • 12
    • 34047269457 scopus 로고    scopus 로고
    • 2-categorification. arXiv: mathRT/0407205, to appear in Ann. of Math., 2007.
    • 2-categorification. arXiv: mathRT/0407205, to appear in Ann. of Math., 2007.
  • 13
    • 84942964111 scopus 로고
    • Finite-dimensional algebras and highest weight categories
    • E. Cline, B. Parshall, and L. Scott. Finite-dimensional algebras and highest weight categories. J. Reine Angew. Math. 391 (1988), 85-99.
    • (1988) J. Reine Angew. Math , vol.391 , pp. 85-99
    • Cline, E.1    Parshall, B.2    Scott, L.3
  • 14
    • 84972570584 scopus 로고
    • A decomposition theorem for certain self-dual modules in the category O
    • D. H. Collingwood and R. S. Irving. A decomposition theorem for certain self-dual modules in the category O. Duke Math. J. 58 (1989), 89-102.
    • (1989) Duke Math. J , vol.58 , pp. 89-102
    • Collingwood, D.H.1    Irving, R.S.2
  • 15
    • 0000890216 scopus 로고
    • On some geometric aspects of Bruhat orderings. II. The parabolic analogue of Kazhdan-Lusztig polynomials
    • V. Deodhar. On some geometric aspects of Bruhat orderings. II. The parabolic analogue of Kazhdan-Lusztig polynomials. J. Algebra 111 (1987), 483-506.
    • (1987) J. Algebra , vol.111 , pp. 483-506
    • Deodhar, V.1
  • 18
    • 84972553715 scopus 로고
    • Quasi-hereditary algebras
    • V. Dlab and C. M. Ringel. Quasi-hereditary algebras. Illinois J. Math. 33 (1989), 280-291.
    • (1989) Illinois J. Math , vol.33 , pp. 280-291
    • Dlab, V.1    Ringel, C.M.2
  • 19
    • 4043115633 scopus 로고    scopus 로고
    • The geometry of generalized Steinberg varieties
    • J. M. Douglass and G. Röhrle. The geometry of generalized Steinberg varieties. Adv. Math. 187 (2004), 396-416.
    • (2004) Adv. Math , vol.187 , pp. 396-416
    • Douglass, J.M.1    Röhrle, G.2
  • 20
    • 34047248923 scopus 로고    scopus 로고
    • Homology of generalized Steinberg varieties and Weyl group invariants
    • arXiv:math.RT/0505567
    • J. M. Douglass and G. Röhrle. Homology of generalized Steinberg varieties and Weyl group invariants. arXiv:math.RT/0505567, 2005.
    • (2005)
    • Douglass, J.M.1    Röhrle, G.2
  • 22
    • 0032282754 scopus 로고    scopus 로고
    • I. B. Frenkel, M. G. Khovanov, and A. A. Kirillov, Jr. Kazhdan-Lusztig polynomials and canonical basis. Transform. Groups 3 (1998), 321-336.
    • I. B. Frenkel, M. G. Khovanov, and A. A. Kirillov, Jr. Kazhdan-Lusztig polynomials and canonical basis. Transform. Groups 3 (1998), 321-336.
  • 23
    • 0004233493 scopus 로고    scopus 로고
    • 2nd ed, Ergeb. Math. Grenzgeb. 2, Springer, Berlin
    • W. Fulton. Intersection Theory. 2nd ed., Ergeb. Math. Grenzgeb. 2, Springer, Berlin, 1998.
    • (1998) Intersection Theory
    • Fulton, W.1
  • 24
    • 0345414176 scopus 로고    scopus 로고
    • On the category O for rational Cherednik algebras
    • V. Ginzburg, N. Guay, E. Opdam, and R. Rouquier. On the category O for rational Cherednik algebras. Invent. Math. 154 (2003), 617-651.
    • (2003) Invent. Math , vol.154 , pp. 617-651
    • Ginzburg, V.1    Guay, N.2    Opdam, E.3    Rouquier, R.4
  • 25
    • 0003833535 scopus 로고
    • Res. Notes in Math. 54, Pitman, Boston, MA
    • H. Miller. Geometry of Coxeter Groups. Res. Notes in Math. 54, Pitman, Boston, MA, 1982.
    • (1982) Geometry of Coxeter Groups
    • Miller, H.1
  • 26
    • 24144436673 scopus 로고    scopus 로고
    • An invariant of link cobordisms from Khovanov homology
    • M. Jacobsson. An invariant of link cobordisms from Khovanov homology. Algebr. Geom. Topol. 4 (2004), 1211-1251.
    • (2004) Algebr. Geom. Topol , vol.4 , pp. 1211-1251
    • Jacobsson, M.1
  • 29
    • 0001239433 scopus 로고
    • The Enright functor on the Bernstein-Gel'fand-Gel'fand category
    • A. Joseph. The Enright functor on the Bernstein-Gel'fand-Gel'fand category O. Invent. Math. 67 (1982), 423-445.
    • (1982) O. Invent. Math , vol.67 , pp. 423-445
    • Joseph, A.1
  • 30
    • 84974000954 scopus 로고
    • On crystal bases of the Q-analogue of universal enveloping algebras
    • M. Kashiwara. On crystal bases of the Q-analogue of universal enveloping algebras. Duke Math. J. 63 (1991), 465-516.
    • (1991) Duke Math. J , vol.63 , pp. 465-516
    • Kashiwara, M.1
  • 31
    • 34250264460 scopus 로고
    • Representations of Coxeter groups and Hecke algebras
    • D. Kazhdan and G. Lusztig. Representations of Coxeter groups and Hecke algebras. Invent. Math. 53 (1979), 165-184.
    • (1979) Invent. Math , vol.53 , pp. 165-184
    • Kazhdan, D.1    Lusztig, G.2
  • 32
    • 13244265682 scopus 로고    scopus 로고
    • On Arkhipov's and Enright's functors
    • O. Khomenko and V. Mazorchuk. On Arkhipov's and Enright's functors. Math. Z. 249 (2005), 357-386.
    • (2005) Math. Z , vol.249 , pp. 357-386
    • Khomenko, O.1    Mazorchuk, V.2
  • 33
    • 30744469864 scopus 로고    scopus 로고
    • An invariant of tangle cobordisms
    • M. Khovanov. An invariant of tangle cobordisms. Trans. Amer. Math. Soc. 358 (2006), 315-327.
    • (2006) Trans. Amer. Math. Soc , vol.358 , pp. 315-327
    • Khovanov, M.1
  • 34
    • 0035998093 scopus 로고    scopus 로고
    • Enright's completions and injectively copre-sented modules
    • S. König and V. Mazorchuk. Enright's completions and injectively copre-sented modules. Trans. Amer. Math. Soc. 354 (2002), 2725-2743.
    • (2002) Trans. Amer. Math. Soc , vol.354 , pp. 2725-2743
    • König, S.1    Mazorchuk, V.2
  • 35
    • 84968495738 scopus 로고
    • Canonical bases arising from quantized enveloping algebras
    • G. Lusztig. Canonical bases arising from quantized enveloping algebras. J. Amer. Math. Soc. 3 (1990), 447-498.
    • (1990) J. Amer. Math. Soc , vol.3 , pp. 447-498
    • Lusztig, G.1
  • 36
    • 0026774287 scopus 로고
    • Canonical bases in tensor products
    • G. Lusztig. Canonical bases in tensor products. Proc. Nat. Acad. Sci. U.S.A. 89 (1992), 8177-8179.
    • (1992) Proc. Nat. Acad. Sci. U.S.A , vol.89 , pp. 8177-8179
    • Lusztig, G.1
  • 38
    • 0037441180 scopus 로고    scopus 로고
    • Tensor product varieties and crystals: The ADE case
    • A. Malkin. Tensor product varieties and crystals: the ADE case. Duke Math. J. 116 (2003), 477-524.
    • (2003) Duke Math. J , vol.116 , pp. 477-524
    • Malkin, A.1
  • 39
    • 34047262191 scopus 로고    scopus 로고
    • Quadratic duals, Koszul dual functors and applications
    • math.RT/0603475
    • V. Mazorchuk, S. Ovsienko, and C. Stroppel. Quadratic duals, Koszul dual functors and applications. math.RT/0603475, 2005.
    • (2005)
    • Mazorchuk, V.1    Ovsienko, S.2    Stroppel, C.3
  • 40
    • 22544463624 scopus 로고    scopus 로고
    • Translation and shuffling of projectively presentable modules and a categorification of a parabolic Hecke module
    • V. Mazorchuk and C. Stroppel. Translation and shuffling of projectively presentable modules and a categorification of a parabolic Hecke module. Trans. Amer. Math. Soc. 357 (2005), 2939-2973.
    • (2005) Trans. Amer. Math. Soc , vol.357 , pp. 2939-2973
    • Mazorchuk, V.1    Stroppel, C.2
  • 41
    • 0035623579 scopus 로고    scopus 로고
    • Quiver varieties and tensor products
    • H. Nakajima. Quiver varieties and tensor products. Invent. Math. 146 (2001), 399-449.
    • (2001) Invent. Math , vol.146 , pp. 399-449
    • Nakajima, H.1
  • 42
    • 1542290643 scopus 로고    scopus 로고
    • Koszul duality of translation- and Zuckerman functors
    • S. Ryom-Hansen. Koszul duality of translation- and Zuckerman functors. J. Lie. Theory 14 (2004), 151-163.
    • (2004) J. Lie. Theory , vol.14 , pp. 151-163
    • Ryom-Hansen, S.1
  • 43
    • 0042706453 scopus 로고    scopus 로고
    • 2) via quivers
    • 2) via quivers. Adv. Math. 177 (2003), 297-340.
    • (2003) Adv. Math , vol.177 , pp. 297-340
    • Savage, A.1
  • 44
    • 84968487223 scopus 로고
    • Kategorie O, perverse Garben und Moduln über den Koinvarianten zur Weylgruppe
    • W. Soergel. Kategorie O, perverse Garben und Moduln über den Koinvarianten zur Weylgruppe. J. Amer. Math. Soc. 3 (1990), 421-445.
    • (1990) J. Amer. Math. Soc , vol.3 , pp. 421-445
    • Soergel, W.1
  • 45
    • 0141815096 scopus 로고
    • The combinatorics of Harish-Chandra bimodules
    • W. Soergel. The combinatorics of Harish-Chandra bimodules. J. Reine Angew. Math. 429 (1992), 49-74.
    • (1992) J. Reine Angew. Math , vol.429 , pp. 49-74
    • Soergel, W.1
  • 46
    • 85009830213 scopus 로고    scopus 로고
    • Kazhdan-Lusztig polynomials and a combinatorics for tilting modules
    • W. Soergel. Kazhdan-Lusztig polynomials and a combinatorics for tilting modules. Represent. Theory 1 (1997), 83-114.
    • (1997) Represent. Theory , vol.1 , pp. 83-114
    • Soergel, W.1
  • 47
    • 0141726794 scopus 로고    scopus 로고
    • Category O: Gradings and translation functors
    • C. Stroppel. Category O: Gradings and translation functors. J. Algebra 268 (2003), 301-326.
    • (2003) J. Algebra , vol.268 , pp. 301-326
    • Stroppel, C.1
  • 48
    • 15744392080 scopus 로고    scopus 로고
    • Categorification of the Temperley-Lieb category, tangles, and cobordisms via projective functors
    • C. Stroppel. Categorification of the Temperley-Lieb category, tangles, and cobordisms via projective functors. Duke Math. J. 126 (2005), 547-596.
    • (2005) Duke Math. J , vol.126 , pp. 547-596
    • Stroppel, C.1
  • 49
    • 34047257205 scopus 로고    scopus 로고
    • TQFT with corners and tilting functors in the Kac-Moody case
    • math.RT/0605103
    • C. Stroppel. TQFT with corners and tilting functors in the Kac-Moody case. math.RT/0605103.
    • Stroppel, C.1
  • 50
    • 34047256436 scopus 로고    scopus 로고
    • In preparation
    • J. Sussan. In preparation, 2005.
    • (2005)
    • Sussan, J.1
  • 51
    • 22744456420 scopus 로고    scopus 로고
    • On characteristic modules of graded quasi-hereditary algebras
    • B. Zhu. On characteristic modules of graded quasi-hereditary algebras. Comm. Algebra 32 (2004), 2919-2928.
    • (2004) Comm. Algebra , vol.32 , pp. 2919-2928
    • Zhu, B.1


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