Su un teorema di Ariki

Michela Varagnolo

Matematica, Cultura e Società. Rivista dell'Unione Matematica Italiana (2018)

  • Volume: 3, Issue: 1, page 31-44
  • ISSN: 2499-751X

Abstract

top
In this note we introduce the reader to the representation theory. We present a result of Ariki (1996) which gives a flavour of the modern way to study it, using interactions between different theories (representations of groups, associative algebras, Lie algebras), and with geometry (but we do not insist on this latter).

How to cite

top

Varagnolo, Michela. "Su un teorema di Ariki." Matematica, Cultura e Società. Rivista dell'Unione Matematica Italiana 3.1 (2018): 31-44. <http://eudml.org/doc/294071>.

@article{Varagnolo2018,
abstract = {In questa nota si vuole introdurre il lettore alla teoria delle rappresentazioni. Presenteremo un risultato di Ariki del 1996, un esempio delle tecniche recenti che usano le interazioni tra le differenti teorie (rappresentazioni di gruppi, di algebre associative, di algebre di Lie) e con la geometria (ma faremo solo un cenno alla fine su quest'ultimo punto).},
author = {Varagnolo, Michela},
journal = {Matematica, Cultura e Società. Rivista dell'Unione Matematica Italiana},
language = {ita},
month = {4},
number = {1},
pages = {31-44},
publisher = {Unione Matematica Italiana},
title = {Su un teorema di Ariki},
url = {http://eudml.org/doc/294071},
volume = {3},
year = {2018},
}

TY - JOUR
AU - Varagnolo, Michela
TI - Su un teorema di Ariki
JO - Matematica, Cultura e Società. Rivista dell'Unione Matematica Italiana
DA - 2018/4//
PB - Unione Matematica Italiana
VL - 3
IS - 1
SP - 31
EP - 44
AB - In questa nota si vuole introdurre il lettore alla teoria delle rappresentazioni. Presenteremo un risultato di Ariki del 1996, un esempio delle tecniche recenti che usano le interazioni tra le differenti teorie (rappresentazioni di gruppi, di algebre associative, di algebre di Lie) e con la geometria (ma faremo solo un cenno alla fine su quest'ultimo punto).
LA - ita
UR - http://eudml.org/doc/294071
ER -

References

top
  1. ARIKI, S., On the decomposition numbers of the Hecke algebra of G ( m ; 1 ; n ) , J. Math. Kyoto Univ., 36 (4) (1996), 789-808. Zbl0888.20011MR1443748DOI10.1215/kjm/1250518452
  2. CHRISS, N., GINZBURG, , Representation Theory and Complex Geometry, Birkhäuser (1997). Zbl0879.22001MR1433132
  3. DIPPER, R., JAMES, G.D., Representations of Hecke algebras of general linear groups, Proc. London Math. Soc., 52 (1986), 20-52. Zbl0587.20007MR812444DOI10.1112/plms/s3-52.1.20
  4. ELIAS, B., WILLIAMSON, G., The Hodge Theory of Soergel bimodules, Annals of Maths.180 (2014), 1-48. Zbl1326.20005MR3245013DOI10.4007/annals.2014.180.3.6
  5. GECK, M., HISS, G., MALLE, G., Towards a classification of the irreducible representations in non-describing characteristic of a finite group of Lie type, Math. Z.221 (1996), no. 3, 353-386. Zbl0858.20008MR1381586DOI10.1007/PL00004253
  6. GOODMAN, F., WENZL, H., Crystal bases of quantum affine algebras and affine Kazhdan-Lusztig polynomials, Internat. Math. Res. Notices, 5 (1999), 251-275. Zbl1027.17011MR1675980DOI10.1155/S1073792899000136
  7. HAYASHI, T., q-analogue of Clifford and Weil algebras-Spinor and oscillator representations of quantum enveloping algebra, Comm. Math. Phys., 127 (1999), 129-144. Zbl0701.17008MR1036118
  8. HUMPHREYS, J. E., Introduction to Lie Algebras and Representation Theory, Springer-Verlag, third printing, revised (1980). Zbl0447.17002MR499562
  9. HUMPHREYS, J. E., Reflection Groups and Coxeter Groups, Cambride University Press (1990). Zbl0725.20028MR1066460DOI10.1017/CBO9780511623646
  10. JAMERS, G., The decomposition matrices of G L n ( q ) for n 10 , Proc. Lond. Math. Soc., 60 (1990), 225-265. MR1031453DOI10.1112/plms/s3-60.2.225
  11. JIMBO, M., A q-analogue of U ( 𝔤 𝔩 ( N + 1 ) ) , Hecke algebra and the Yang-Baxter equation, Lett. Math. Phys., 11 (1986), 247-252. Zbl0602.17005MR841713DOI10.1007/BF00400222
  12. JONES, V. F. R., Hecke algebra representations of braid groups, Annals of Math., 126 (2) (1987), 335-388. Zbl0631.57005MR908150DOI10.2307/1971403
  13. JIMBO, M., MISRA, K., MIWA, T., OKADO, M., Combinatorics of representations of U q ( 𝔰 𝔩 ^ ( n ) ) at q = 0 , Comm. Math. Phys., 136 (1991), 543-566. Zbl0749.17015MR1099695
  14. KASHIWARA, M., On crystal bases of q-analogue of universal enveloping algebra, Duke Math. J., 63 (1991), 465-516. Zbl0739.17005MR1115118DOI10.1215/S0012-7094-91-06321-0
  15. KASHIWARA, M., On crystal bases, CMS Conf. Proc., 16 (1995), 155-197. Zbl0851.17014MR1357199
  16. KAC, V.G., Infinite Dimensional Lie Algebras (third edition), Cambridge University Press, (1990). Zbl0716.17022MR1104219DOI10.1017/CBO9780511626234
  17. KRONHEIMER, P.B., MROWKA, T. S., Khovanov homology is an unknot-detector, Publ. Math. Inst. Hautes Études Sci., 113 (2011), 97-208. Zbl1241.57017MR2805599DOI10.1007/s10240-010-0030-y
  18. LASCOUX, A., LECLERC, B., THIBON, J-Y., Hecke algebras at roots of unity and crystal bases of quantum affine algebras, Commun. Math. Phys., 181 (1996), 205-263. Zbl0874.17009MR1410572
  19. MISRA, K., MIWA, T., Crystal base for the basic representation of U q ( 𝔰 𝔩 ^ ( n ) ) , Comm. Math. Phys., 134 (1990), 79-88. Zbl0724.17010MR1079801
  20. SAGAN, B. E., The Symmetric Group. Representations, Combinatorial Algorithms, and Symmetric Functions, GTMSpringer (2001). Zbl0964.05070MR1824028DOI10.1007/978-1-4757-6804-6
  21. VARAGNOLO, M., VASSEROT, E., On the decomposition matrices of the quantized Schur algebra, Duke Math. J., 100 (1999), 267-297. Zbl0962.17006MR1722955DOI10.1215/S0012-7094-99-10010-X
  22. WILLIAMSON, G., Schubert calculus and torsion explosion, J. AMS, 30 (2017), 1023-1046. Zbl1380.20015MR3671935DOI10.1090/jams/868

NotesEmbed ?

top

You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.

    
                

Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.