Conformal blocks in the tensor product of vector representations and localization formulas

R. Rimányi[1]; A. Varchenko[1]

  • [1] Department of Mathematics, University of North Carolina at Chapel Hill, USA

Annales de la faculté des sciences de Toulouse Mathématiques (2011)

  • Volume: 20, Issue: 1, page 71-97
  • ISSN: 0240-2963

Abstract

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Using equivariant localization formulas we give a formula for conformal blocks at level one on the sphere as suitable polynomials.

How to cite

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Rimányi, R., and Varchenko, A.. "Conformal blocks in the tensor product of vector representations and localization formulas." Annales de la faculté des sciences de Toulouse Mathématiques 20.1 (2011): 71-97. <http://eudml.org/doc/219815>.

@article{Rimányi2011,
abstract = {Using equivariant localization formulas we give a formula for conformal blocks at level one on the sphere as suitable polynomials.},
affiliation = {Department of Mathematics, University of North Carolina at Chapel Hill, USA; Department of Mathematics, University of North Carolina at Chapel Hill, USA},
author = {Rimányi, R., Varchenko, A.},
journal = {Annales de la faculté des sciences de Toulouse Mathématiques},
keywords = {conformal blocks; Lie algebras; localizations; divided differences},
language = {eng},
month = {1},
number = {1},
pages = {71-97},
publisher = {Université Paul Sabatier, Toulouse},
title = {Conformal blocks in the tensor product of vector representations and localization formulas},
url = {http://eudml.org/doc/219815},
volume = {20},
year = {2011},
}

TY - JOUR
AU - Rimányi, R.
AU - Varchenko, A.
TI - Conformal blocks in the tensor product of vector representations and localization formulas
JO - Annales de la faculté des sciences de Toulouse Mathématiques
DA - 2011/1//
PB - Université Paul Sabatier, Toulouse
VL - 20
IS - 1
SP - 71
EP - 97
AB - Using equivariant localization formulas we give a formula for conformal blocks at level one on the sphere as suitable polynomials.
LA - eng
KW - conformal blocks; Lie algebras; localizations; divided differences
UR - http://eudml.org/doc/219815
ER -

References

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  1. Askey. (R.).— Some basic hypergeometric extensions of integrals of Selberg and Andrews. SIAM J. Math. Anal., 11, p. 938-951, (1980). Zbl0458.33002MR595822
  2. Atiyah (M. F.) Bott (R.).— The moment map and equivariant cohomology. Topology, Vol. 23, Issue 3, p. 1–28, (1984). Zbl0521.58025MR721448
  3. Feigin (B.), Schechtman (V.), Varchenko (A.).— On algebraic equations satisfied by hypergeometric correlators in WZW models. I, Comm. Math. Phys. 163, p. 173–184, (1994). Zbl0835.17019MR1277938
  4. Feigin (B.), Schechtman (V.), Varchenko (A.).— On algebraic equations satisfied by hypergeometric correlators in WZW models. II, Comm. in Math. Phys. v. 170, No. 1, p. 219–247; math.hep-th/9407010, (1994). Zbl0842.17043MR1331699
  5. Felder (G.), Stevens (L.), Varchenko (A.).— Elliptic Selberg integrals and conformal blocks. Math. Res. Lett. 10, no. 5-6, p. 671–684, (2003). Zbl1041.33003MR2024724
  6. Gusein-Zade (S.), Varchenko (A.).— Verlinde algebras and the intersection form on vanishing cycles. Selecta Math. (N.S.) 3, no. 1, p. 79–97, (1997). Zbl0911.32044MR1454086
  7. Kazhdan (D.), Lusztig (G.).— Tensor categories arising from affine Lie algebras I-V. J. Amer. Math. Soc., 6, p. 905–947, 1993 ; ibid., p. 949–1011 ; 7, p. 335–381 ; ibid., p. 383–454, (1994). Zbl0786.17017
  8. Knizhnik (V.G.), Zamolodchikov (A.B.).— Current Algebra and Wess-Zumino Model in Two-Dimensions. Nucl. Phys. B 247, p. 83–103, (1984). Zbl0661.17020MR853258
  9. Lascoux(A.).— Symmetric Functions and Combinatorial Operations on Polynomials. CMBS 99, AMS, (2003). Zbl1039.05066
  10. Looijenga (E.), Varchenko (A.).— Unitarity of SL ( 2 ) -conformal blocks in genus zero. arXiv:0810.4310, [v1], p. 1–15. 
  11. Mukhin (E.), Varchenko (A.).— Remarks on critical points of phase functions and norms of Bethe vectors; Arrangements—Tokyo 1998, p. 239–246, Adv. Stud. Pure Math., 27, Kinokuniya, Tokyo, (2000). Zbl1040.17001MR1796902
  12. Mukhin (E.), Varchenko (A.).— Norm of a Bethe vector and the Hessian of the master function. Compos. Math. 141, no. 4, p. 1012–1028, (2005). Zbl1072.82012MR2148192
  13. Opdam (E.).— Some applications of hypergeometric shift operators. Invent. Math. 98, no. 1, 118, (1989). Zbl0696.33006MR1010152
  14. Ramadas (T. R.).— The “Harder-Narasimhan trace” and unitarity of the KZ/Hitchin connection: genus 0. Ann. of Math. (2) 169, no. 1, p. 1–39, (2009). Zbl1167.32011MR2480600
  15. Reshetikhin (N.), Varchenko (A.).— Quasiclassical asymptotics of solutions to the KZ equations. Geometry, topology, & physics, p. 293–322, Conf. Proc. Lecture Notes Geom. Topology, IV, Int. Press, Cambridge, MA, (1995). Zbl0867.58065MR1358621
  16. Rimányi (R.), Schechtman (V.), Varchenko (A.).— Conformal blocks and equivariant cohomology. In preparation. 
  17. Selberg (A.).— Bemerkninger om et multiplet integral. Norsk Mat. Tidsskr. 26, p. 71–78, (1944). Zbl0063.06870MR18287
  18. Spiridonov (V.).— An elliptic beta integral. New trends in difference equations (Temuco, 2000), p. 273– 282, Taylor and Francis, London, (2002). Zbl1065.33015MR2016068
  19. Schechtman (V.), Varchenko (A.).— Arrangements of Hyperplanes and Lie Algebra Homology. Invent. Math. Vol. 106, p. 139–194, (1991). Zbl0754.17024MR1123378
  20. Tarasov (V.), Varchenko (A.).— Selberg-type integrals associated with s l 3 , Lett. Math. Phys. 65, no. 3, p. 173–185, (2003). Zbl1055.33016MR2033704
  21. Varchenko (A.).— A Selberg Integral Type Formula for an s l 2 One-Dimensional Space of Conformal Blocks. arXiv:0810.3355, (2008). 
  22. Warnaar (O.).— A Selberg integral for the Lie algebra A n , arXiv:0708.1193, p. 1–32. Zbl1243.33053
  23. Zuber (J.-B.).— Graphs and reflection groups. Comm. Math. Phys. 179, no. 2, p. 265–294, (1996). Zbl0942.20018MR1400741

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