Work of Vyjayanthi Chari. (English) Zbl 1523.17001
Greenstein, Jacob (ed.) et al., Interactions of quantum affine algebras with cluster algebras, current algebras and categorification. In honor of Vyjayanthi Chari on the occasion of her 60th birthday. Based on the summer school and the conference, Washington, DC, USA, June 2018. Cham: Birkhäuser. Prog. Math. 337, 69-75 (2021).
Summary: The goal of this survey is to describe the most important contributions of Vjyayanthi Chari in representation theory.
For the entire collection see [Zbl 1481.17001].
For the entire collection see [Zbl 1481.17001].
MSC:
| 17-03 | History of nonassociative rings and algebras |
| 01A70 | Biographies, obituaries, personalia, bibliographies |
References:
| [1] | Beck, J.; Chari, V.; Pressley, A., An algebraic characterization of the affine canonical basis, Duke Math. J., 99, 3, 455-487 (1999) · Zbl 0964.17013 · doi:10.1215/S0012-7094-99-09915-5 |
| [2] | M. Bennett, A. Berenstein, V. Chari, A. Khoroshkin, and S. Loktev, Macdonald polynomials and BGG reciprocity for current algebras, Selecta Math. (N.S.) 20 (2014), no. 2, 585-607, doi:10.1007/s00029-013-0141-7. · Zbl 1367.17017 |
| [3] | M. Bennett and V. Chari, Tilting modules for the current algebra of a simple Lie algebra, Recent developments in Lie algebras, groups and representation theory, Proc. Sympos. Pure Math., vol. 86, Amer. Math. Soc., Providence, RI, 2012, pp. 75-97, doi:10.1090/pspum/086/1411. · Zbl 1317.17016 |
| [4] | Bennett, M.; Chari, V.; Manning, N., BGG reciprocity for current algebras, Adv. Math., 231, 1, 276-305 (2012) · Zbl 1292.17015 · doi:10.1016/j.aim.2012.05.005 |
| [5] | R. Biswal, V. Chari, and D. Kus, Demazure flags, q-Fibonacci polynomials and hypergeometric series, Res. Math. Sci. 5 (2018), no. 1, Paper No. 12, 34, doi:10.1007/s40687-018-0129-1. · Zbl 1473.17022 |
| [6] | R. Biswal, V. Chari, P. Shereen, and J. Wand, Macdonald Polynomials and level two Demazure modules for affine \(\mathfrak{sl}_{\text{n}+1} \) , available at arXiv:1910.0548. · Zbl 1489.17014 |
| [7] | Brito, M.; Chari, V., Tensor products and q-characters of HL-modules and monoidal categorifications,, J. Éc. Polytech. Math., 6, 581-619 (2019) · Zbl 1446.17026 · doi:10.5802/jep.101 |
| [8] | M. Brito and V. Chari,, Resolutions and a Weyl Character formula for prime representations of quantum affine \(\mathfrak{sl}_{\text{n}+1} \) , available at arXiv:1704.02520. |
| [9] | Chari, V., Annihilators of Verma modules for Kac-Moody Lie algebras, Invent. Math., 81, 1, 47-58 (1985) · Zbl 0584.17008 · doi:10.1007/BF01388771 |
| [10] | Chari, V., Integrable representations of a?ne Lie algebras, Invent. Math., 85, 2, 317-335 (1986) · Zbl 0603.17011 · doi:10.1007/BF01389093 |
| [11] | Chari, V., Minimal affinizations of representations of quantum groups: the rank 2 case, Publ. Res. Inst. Math. Sci., 31, 5, 873-911 (1995) · Zbl 0855.17010 · doi:10.2977/prims/1195163722 |
| [12] | Chari, V., On the fermionic formula and the Kirillov-Reshetikhin conjecture, Internat. Math. Res. Notices, 12, 629-654 (2001) · Zbl 0982.17004 · doi:10.1155/S1073792801000332 |
| [13] | Chari, V., Braid group actions and tensor products, Int. Math. Res. Not., 7, 357-382 (2002) · Zbl 0990.17009 · doi:10.1155/S107379280210612X |
| [14] | Chari, V.; Fourier, G.; Khandai, T., A categorical approach to Weyl modules, Transform. Groups, 15, 3, 517-549 (2010) · Zbl 1245.17004 · doi:10.1007/s00031-010-9090-9 |
| [15] | Chari, V.; Greenstein, J., Current algebras, highest weight categories and quivers, Adv. Math., 216, 2, 811-840 (2007) · Zbl 1222.17010 · doi:10.1016/j.aim.2007.06.006 |
| [16] | Chari, V.; Greenstein, J., Graded level zero integrable representations of affine Lie algebras, Trans. Amer. Math. Soc., 360, 6, 2923-2940 (2008) · Zbl 1195.17017 · doi:10.1090/S0002-9947-07-04394-2 |
| [17] | Chari, V.; Greenstein, J., A family of Koszul algebras arising from finite-dimensional representations of simple Lie algebras, Adv. Math., 220, 4, 1193-1221 (2009) · Zbl 1165.17005 · doi:10.1016/j.aim.2008.11.007 |
| [18] | Chari, V.; Greenstein, J., Minimal affinizations as projective objects, J. Geom. Phys., 61, 3, 594-609 (2011) · Zbl 1207.81040 · doi:10.1016/j.geomphys.2010.11.008 |
| [19] | Chari, V.; Ilangovan, S., On the Harish-Chandra homomorphism for infinite-dimensional Lie algebras, J. Algebra, 90, 2, 476-490 (1984) · Zbl 0545.17003 · doi:10.1016/0021-8693(84)90185-6 |
| [20] | Chari, V.; Ion, B., BGG reciprocity for current algebras, Compos. Math., 151, 7, 1265-1287 (2015) · Zbl 1337.17016 · doi:10.1112/S0010437X14007908 |
| [21] | V. Chari and S. Loktev, Weyl, Demazure and fusion modules for the current algebra of \(\mathfrak{sl}_{\text{r}+1} \) , Adv. Math. 207 (2006), no. 2, 928-960, doi:10.1016/j.aim.2006.01.012. · Zbl 1161.17318 |
| [22] | Chari, V.; Moura, A., Characters and blocks for finite-dimensional representations of quantum affine algebras, Int. Math. Res. Not., 5, 257-298 (2005) · Zbl 1074.17004 · doi:10.1155/IMRN.2005.257 |
| [23] | Chari, V.; Moura, A., The restricted Kirillov-Reshetikhin modules for the current and twisted current algebras, Comm. Math. Phys., 266, 2, 431-454 (2006) · Zbl 1118.17007 · doi:10.1007/s00220-006-0032-2 |
| [24] | V. Chari, A. Moura, and C. Young, Prime representations from a homological perspective, Math. Z. 274 (2013), no. 1-2, 613-645, doi:10.1007/s00209-012-. · Zbl 1369.17008 |
| [25] | Chari, V.; Pressley, A., New unitary representations of loop groups, Math. Ann., 275, 1, 87-104 (1986) · Zbl 0603.17012 · doi:10.1007/BF01458586 |
| [26] | Chari, V.; Pressley, A., A new family of irreducible, integrable modules for affine Lie algebras, Math. Ann., 277, 3, 543-562 (1987) · Zbl 0608.17009 · doi:10.1007/BF01458331 |
| [27] | Chari, V.; Pressley, A., Integrable representations of twisted affine Lie algebras, J. Algebra, 113, 2, 438-464 (1988) · Zbl 0661.17023 · doi:10.1016/0021-8693(88)90171-8 |
| [28] | Chari, V.; Pressley, A., Fundamental representations of Yangians and singularities of R-matrices,, J. Reine Angew. Math., 417, 87-128 (1991) · Zbl 0726.17014 |
| [29] | Chari, V.; Pressley, A., Quantum affine algebras, Comm. Math. Phys., 142, 2, 261-283 (1991) · Zbl 0739.17004 · doi:10.1007/BF02102063 |
| [30] | Chari, V.; Pressley, A., A guide to quantum groups (1994), Cambridge: Cambridge University Press, Cambridge · Zbl 0839.17009 |
| [31] | V. Chari and A. Pressley, Quantum affine algebras and their representations, Representations of groups (Banff, AB, 1994), CMS Conf. Proc., vol. 16, Amer. Math. Soc., Providence, RI, 1995, pp. 59-78. · Zbl 0855.17009 |
| [32] | V. Chari and A. Pressley, Yangians: their representations and characters, Acta Appl. Math. 44 (1996), no. 1-2, 39-58, doi:10.1007/BF00116515. Representations of Lie groups, Lie algebras and their quantum analogues. · Zbl 0876.17013 |
| [33] | V. Chari and A. Pressley, Quantum affine algebras and integrable quantum systems, Quantum fields and quantum space time (Cargèse, 1996), NATO Adv. Sci. Inst. Ser. B Phys., vol. 364, Plenum, New York, 1997, pp. 245-263. · Zbl 0967.17014 |
| [34] | V. Chari and A. Pressley, Weyl modules for classical and quantum affine algebras, Represent. Theory 5 (2001), 191-223, doi:10.1090/S1088-4165-01-. · Zbl 0989.17019 |
| [35] | V. Chari and A. Pressley, Integrable and Weyl modules for quantum affine sl_2 , Quantum groups and Lie theory (Durham, 1999), London Math. Soc. Lecture Note Ser., vol. 290, Cambridge Univ. Press, Cambridge, 2001, pp. 48-62. · Zbl 1034.17008 |
| [36] | M. Duflo, Sur la classification des idéaux primitifs dans l’algèbre enveloppante d’une algèbre de Lie semi-simple, Ann. of Math. (2) 105 (1977), no. 1, 107-120, doi:10.2307/1971027. · Zbl 0346.17011 |
| [37] | Hernandez, D.; Leclerc, B., Cluster algebras and quantum a?ne algebras, Duke Math. J., 154, 2, 265-341 (2010) · Zbl 1284.17010 · doi:10.1215/00127094-2010-040 |
| [38] | Kang, S-J; Kashiwara, M.; Kim, M., Symmetric quiver Hecke algebras and R-matrices of quantum affine algebras, Invent. Math., 211, 2, 591-685 (2018) · Zbl 1407.81108 · doi:10.1007/s00222-017-0754-0 |
| [39] | Kashiwara, M.; Kim, M.; Oh, S.; Park, E., Monoidal categorification and quantum affine algebras, Compos. Math., 156, 5, 1039-1077 (2020) · Zbl 1497.17020 · doi:10.1112/S0010437X20007137 |
| [40] | Khovanov, M.; Lauda, A. D., A diagrammatic approach to categorification of quantum groups. I, Represent. Theory, 13, 309-347 (2009) · Zbl 1188.81117 · doi:10.1090/S1088-4165-09-00346-X |
| [41] | A. N. Kirillov and N. Yu. Reshetikhin, Representations of Yangians and multiplicities of the inclusion of the irreducible components of the tensor product of representations of simple Lie algebras, Zap. Nauchn. Sem. Leningrad. Otdel. Mat. Inst. Steklov. (LOMI) 160 (1987), no. Anal. Teor. Chisel i Teor. Funktsil̆. 8, 211-221, 301, doi:10.1007/BF02342935. · Zbl 0637.16007 |
| [42] | R. Rouquier, 2-Kac-Moody algebras, available at arXiv:0812.5023. |
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