Affine quivers and canonical bases

George Lusztig

Publications Mathématiques de l'IHÉS (1992)

  • Volume: 76, page 111-163
  • ISSN: 0073-8301

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Lusztig, George. "Affine quivers and canonical bases." Publications Mathématiques de l'IHÉS 76 (1992): 111-163. <http://eudml.org/doc/104082>.

@article{Lusztig1992,
author = {Lusztig, George},
journal = {Publications Mathématiques de l'IHÉS},
keywords = {affine Coxeter graph; quantized enveloping algebra; simple perverse sheaves; canonical basis},
language = {eng},
pages = {111-163},
publisher = {Institut des Hautes Études Scientifiques},
title = {Affine quivers and canonical bases},
url = {http://eudml.org/doc/104082},
volume = {76},
year = {1992},
}

TY - JOUR
AU - Lusztig, George
TI - Affine quivers and canonical bases
JO - Publications Mathématiques de l'IHÉS
PY - 1992
PB - Institut des Hautes Études Scientifiques
VL - 76
SP - 111
EP - 163
LA - eng
KW - affine Coxeter graph; quantized enveloping algebra; simple perverse sheaves; canonical basis
UR - http://eudml.org/doc/104082
ER -

References

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  1. [DR] V. DLAB and C. M. RINGEL, Indecomposable representations of graphs and algebras, Memoirs Amer. Math. Soc., 173 (1976), 1-57. Zbl0332.16015MR56 #5657
  2. [DF] P. DONOVAN and M. R. FREISLICH, The representation theory of finite graphs and associated algebras, Carleton Math. Lect. Notes, 5 (1973). Zbl0304.08006MR50 #9701
  3. [D] V. G. DRINFELD, Quantum groups, Proc. Intern. Congr. Math., Berkeley 1986, Amer. Math. Soc., Providence R.I. (1987), 798-820. Zbl0667.16003MR89f:17017
  4. [GP] I. M. GELFAND and V. A. PONOMAREV, Problems of linear algebra and classification of quadruples of subspaces in a finite dimensional vector space, Coll. Math. Soc. Bolyai (Hungary), 5 (1970), 163-237. Zbl0294.15002MR50 #9896
  5. [Kr] L. KRONECKER, Algebraische Reduktion der Scharen bilinearer Formen, Sitz. Akad. Berlin (1890), 763-776. JFM22.0169.01
  6. [K] P. B. KRONHEIMER, The construction of ALE spaces as hyper-Kähler quotients, Jour. Diff. Geom. 29 (1989), 665-683. Zbl0671.53045MR90d:53055
  7. [L] G. LUSZTIG, Quivers, perverse sheaves and quantized enveloping algebras, Jour. Amer. Math. Soc. 4 (1991), 365-421. Zbl0738.17011MR91m:17018
  8. [MK] J. MCKAY, Graphs, singularities and finite groups, Proc. Symp. Pure Math. 37 (1980), 183-186. Zbl0451.05026MR82e:20014
  9. [N] L. A. NAZAROVA, Representations of quivers of infinite type. Izv. Akad. Nauk SSSR, ser. Math. 37 (1973), 752-791. Zbl0298.15012MR49 #2785
  10. [R1] C. M. RINGEL, Representations of K-species and bimodules, J. of Alg. 41 (1976), 269-302. Zbl0338.16011MR54 #10340
  11. [R2] C. M. RINGEL, From representations of quivers via Hall algebras and Loewy algebras to quantum groups, preprint, Univ. Bielefeld, 1991. 
  12. [R3] C. M. RINGEL, The canonical algebras. In : Topics in Algebra, Banach Center Publications, 26 (1991), 407-432. Zbl0778.16003MR93e:16022
  13. [R4] C. M. RINGEL, The composition algebra of a cyclic quiver, preprint, Univ. Bielefeld, 1992. Zbl0797.16014

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