Book contents
- Frontmatter
- 2010 Mathematics Subject Classification
- Contents
- Introduction
- 1 Preliminaries
- 2 Double Ringel–Hall algebras of cyclic quivers
- 3 Affine quantum Schur algebras and the Schur–Weyl reciprocity
- 4 Representations of affine quantum Schur algebras
- 5 The presentation and realization problems
- 6 The classical (v = 1) case
- Bibliography
- Index
- References
Bibliography
Published online by Cambridge University Press: 05 January 2013
Book contents
- Frontmatter
- 2010 Mathematics Subject Classification
- Contents
- Introduction
- 1 Preliminaries
- 2 Double Ringel–Hall algebras of cyclic quivers
- 3 Affine quantum Schur algebras and the Schur–Weyl reciprocity
- 4 Representations of affine quantum Schur algebras
- 5 The presentation and realization problems
- 6 The classical (v = 1) case
- Bibliography
- Index
- References
Summary
A summary is not available for this content so a preview has been provided. Please use the Get access link above for information on how to access this content.
- Type
- Chapter
- Information
- Publisher: Cambridge University PressPrint publication year: 2012
References
[1] , and , Representation Theory of Artin Algebras, Cambridge Studies in Advanced Mathematics, No. 36, Cambridge University Press, Cambridge, 1995.
[2] , Braid group action and quantum affine algebras, Commun. Math. Phys. 165 (1994), 555–568.Google Scholar
[3] , and , An algebraic characterization of the affine canonical basis, Duke Math. J. 99 (1999), 455–487.Google Scholar
[4] , and , A geometric setting for the quantum deformation of GLn, Duke Math. J. 61 (1990), 655–677.Google Scholar
[7] and , A Guide to Quantum Groups, Cambridge University Press, Cambridge, 1994.
[8] and , Quantum affine algebras and their representations, Representations of Groups (Banff, AB, 1994), CMS Conf. Proc., 16, American Mathematical Society, Providence, RI, 1995, 59–78.
[9] and , Quantum affine algebras and affine Hecke algebras, Pacific J. Math. 174 (1996), 295–326.Google Scholar
[10] and , Quantum affine algebras at roots of unity, Represen. Theory 1 (1997), 280–328.Google Scholar
[12] , , and , Finite Dimensional Algebras and Quantum Groups, Mathematical Surveys and Monographs Volume 150, American Mathematical Society, Providence, RI, 2008.
[13] , and , Generic extensions and canonical bases for cyclic quivers, Can. J. Math. 59 (2007), 1260–1283.Google Scholar
[16] and , q-Tensor spaces and q-Weyl modules, Trans. Amer. Math. Soc. 327 (1991), 251–282.
[17] , The q-Schur algebra, LMS Lecture Note Series 253, Cambridge University Press, Cambridge, 1998.
[20] , A new realization of Yangians and quantized affine algebras, Soviet Math. Dokl. 32 (1988), 212–216.Google Scholar
[21] , Kahzdan–Lusztig bases and isomorphism theorems for q-Schur algebras, Contemp. Math. 139 (1992), 121–140.Google Scholar
[22] , A note on the quantized Weyl reciprocity at roots of unity, Alg. Colloq. 2 (1995), 363–372.Google Scholar
[23] and , Quantum gl∞, infinite q-Schur algebras and their representations, J. Algebra 322 (2009), 1516–1547.Google Scholar
[24] and , A modified BLM approach to quantum affine gln, Math. Z. 266 (2010), 747–781.Google Scholar
[25] , and , Infinitesimal quantum gln and little q-Schur algebras, J. Algebra 287 (2005), 199–233.Google Scholar
[26] and , Monomial bases for q-Schur algebras, Trans. Amer. Math. Soc. 355 (2003), 1593–1620.Google Scholar
[27] , and , Quantum Weyl reciprocity and tilting modules, Commun. Math. Phys. 195 (1998), 321–352.Google Scholar
[29] and , The q-characters of representations of quantum affine algebras and deformations of W-algebras, Contemp. Math., AMS 248 (1998), 163–205.Google Scholar
[32] and , Langlands reciprocity for affine quantum groups of type An, Internat. Math. Res. Not. 3 (1993), 67–85.Google Scholar
[33] , Polynomial Representations of GLn, 2nd edn, with an appendix on Schensted correspondence and Littelmann paths by , and , Lecture Notes in Mathematics, No. 830, Springer-Verlag, Berlin, 2007.
[34] , Hall algebras, hereditary algebras and quantum groups, Invent. Math. 120 (1995), 361–377.Google Scholar
[36] , The Hall polynomials of a cyclic serial algebra, Commun. Algebra 23 (1995) 743–751.CrossRefGoogle Scholar
[37] and , Universal PBW-basis of Hall–Ringel algebras and Hall polynomials, J. Algebra 198 (1997) 339–351.CrossRefGoogle Scholar
[38] and , On Ringel–Hall algebras of tame hereditary algebras, Algebra Represent. Theory 5 (2002), 527–550.Google Scholar
[39] , Symmetric functions and the center of the Ringel–Hall algebra of a cyclic quiver, Math. Z. 251 (2005), 705–719.Google Scholar
[40] , Three presentations of the Hopf algebra Uv(gln), preprint, 2009 (available at http://www1.maths.leeds.ac.uk/~ahubery).
[41] and , On some Bruhat decomposition and the structure of the Hecke rings of p-adic Chevalley groups, Inst. Hautes Études Sci. Publ. Math. 25 (1965), 5–48.Google Scholar
[42] , and , Crystal bases for quantum generalized Kac–Moody algebras, Proc. London Math. Soc. 90 (2005), 395–438.Google Scholar
[43] , A q-analogue of U(gl(N + 1), Hecke algebra, and the Yang–Baxter equation, Lett. Math. Physics 11 (1986), 247–252.Google Scholar
[44] , On Drinfeld realization of quantum affine algebras, in: The Monster and Lie algebras (Columbus, OH, 1996), Ohio State University Mathematical Research Institute Publications, 7, de Gruyter, Berlin, 1998, 195–206.
[45] , A quotient of the affine Hecke algebra in the Brauer algebra, Enseign. Math. 40 (1994), 313–344.Google Scholar
[46] , Quantum Groups and Their Primitive Ideals, Ergebnisse der Mathematik und ihrer Grenzgebiete, Vol. 29, Springer-Verlag, Berlin, 1995.
[47] , Infinite Dimensional Lie Algebras, 3rd edn, Cambridge University Press, Cambridge, 1990.
[48] , Quantum deformations of generalized Kac–Moody algebras and their modules, J. Algebra 175 (1995), 1041–1066.Google Scholar
[49] and , Canonical bases for quantum generalized Kac–Moody algebras, Adv. Math. 200 (2006), 445–478.Google Scholar
[50] and , Representations of Coxeter groups and Hecke algebras, Invent. Math. 53 (1979), 165–184.Google Scholar
[51] , Some examples of square integrable representations of semisimple p-adic groups, Trans. Amer. Math. Soc. 277 (1983), 623–653.Google Scholar
[52] , Finite dimensional Hopf algebras arising from quantized universal enveloping algebras, J. Amer. Math. Soc. 3 (1990), 257–296.Google Scholar
[53] , Quivers, perverse sheaves, and quantized enveloping algebras, J. Amer. Math. Soc. 4 (1991), 365–421.Google Scholar
[54] , Introduction to Quantum Groups, Progress in Math. 110, Birkhäuser,Boston, 1993.
[55] , Canonical bases and Hall algebras, in Representation Theories and Algebraic Geometry, and (eds.), Kluwer, Dordrecht, 1998, 365–399.
[57] , Transfer maps for quantum affine sln, in: Representations and quantizations (Shanghai, 1998), China Higher Education Press, Beijing, 2000, 341–356.
[58] , Generalized q-Schur algebras and quantum Frobenius, Adv. Math. 214 (2007), 116–131.Google Scholar
[59] , Some Hall polynomials for representation-finite trivial extension algebras, J. Algebra 197 (1997), 1–13.Google Scholar
[60] and , Triangulated categories and Kac–Moody algebras, Invent. Math. 140 (2000), 563–603.Google Scholar
[61] , A geometric Schur–Weyl duality for quotients of affine Hecke algebras, J. Algebra 321 (2009), 230–247.Google Scholar
[62] , Generic extensions and multiplicative bases of quantum groups at q = 0, Represent. Theory 5 (2001), 147–163.Google Scholar
[65] , The composition algebra of a cyclic quiver, Proc. London Math. Soc. 66 (1993), 507–537.Google Scholar
[66] , On modules over the Hecke algebra of a p-adic group, Invent. Math. 79 (1985), 443–465.Google Scholar
[67] , The Hall algebra of a cyclic quiver and canonical bases of Fock spaces, Internat. Math. Res. Not. 8 (2000), 413–440.Google Scholar
[68] , Noncommutative projective curves and quantum loop algebras, Duke Math. J. 121 (2004) 113–168.CrossRefGoogle Scholar
[69] , Über eine Klasse von Matrizen, die sich einer gegebenen Matrix zuordnen lassen, Dissertation, Berlin 1902.
[70] , Über die rationalen Darstellungen der allgemeinen linearen Gruppe, Sitzber Königl. Preuß. Ak. Wiss., Physikal.-Math. Klasse, pages 58–75, 1927.
[71] and , On the double of the Hall algebra of a quiver, J. Algebra 221 (1999), 135–160Google Scholar
[72] , Hopf Algebras, Benjamin, New York, 1969.
[73] and , On the decomposition matrices of the quantized Schur algebra, Duke Math. J. 100 (1999), 267–297.Google Scholar
[74] and , From double affine Hecke algebras to quantized affine Schur algebras, Internat. Math. Res. Not. 26 (2004), 1299–1333.Google Scholar
[75] , Affine quantum groups and equivariant K-theory, Transf. Groups 3 (1998), 269–299.Google Scholar
[77] , The Classical Groups, Princeton University Press, Princeton, NJ, 1946.
[78] , Drinfeld double and Ringel–Green theory of Hall algebras, J. Algebra 190 (1997), 100–144.Google Scholar
[80] , On the affine Schur algebra of type A. II, Algebr. Represent. Theory 12 (2009), 63–75.Google Scholar
[81] , Induced representations of reductive p-adic groups II. On irreducible representations of GLn, Ann. Sci. Ec. Norm. Sup. 4e Sér. 13 (1980), 165–210.Google Scholar
[82] , Degenerations for modules over representation-finite biserial algebras, J. Algebra 198 (1997), 563–581.Google Scholar