Quasi-particle fermionic formulas for (k, 3)-admissible configurations
Miroslav Jerković; Mirko Primc
Open Mathematics (2012)
- Volume: 10, Issue: 2, page 703-721
- ISSN: 2391-5455
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topMiroslav Jerković, and Mirko Primc. "Quasi-particle fermionic formulas for (k, 3)-admissible configurations." Open Mathematics 10.2 (2012): 703-721. <http://eudml.org/doc/269365>.
@article{MiroslavJerković2012,
abstract = {We construct new monomial quasi-particle bases of Feigin-Stoyanovsky type subspaces for the affine Lie algebra sl(3;ℂ)∧ from which the known fermionic-type formulas for (k, 3)-admissible configurations follow naturally. In the proof we use vertex operator algebra relations for standard modules and coefficients of intertwining operators.},
author = {Miroslav Jerković, Mirko Primc},
journal = {Open Mathematics},
keywords = {Quasi-particle bases; Feigin-Stoyanovsky type subspaces; Affine Lie algebras; Fermionic-type formulas; Admissible configurations; quasi-particle bases; affine Lie algebras; fermionic-type formulas; admissible configurations},
language = {eng},
number = {2},
pages = {703-721},
title = {Quasi-particle fermionic formulas for (k, 3)-admissible configurations},
url = {http://eudml.org/doc/269365},
volume = {10},
year = {2012},
}
TY - JOUR
AU - Miroslav Jerković
AU - Mirko Primc
TI - Quasi-particle fermionic formulas for (k, 3)-admissible configurations
JO - Open Mathematics
PY - 2012
VL - 10
IS - 2
SP - 703
EP - 721
AB - We construct new monomial quasi-particle bases of Feigin-Stoyanovsky type subspaces for the affine Lie algebra sl(3;ℂ)∧ from which the known fermionic-type formulas for (k, 3)-admissible configurations follow naturally. In the proof we use vertex operator algebra relations for standard modules and coefficients of intertwining operators.
LA - eng
KW - Quasi-particle bases; Feigin-Stoyanovsky type subspaces; Affine Lie algebras; Fermionic-type formulas; Admissible configurations; quasi-particle bases; affine Lie algebras; fermionic-type formulas; admissible configurations
UR - http://eudml.org/doc/269365
ER -
References
top- [1] Ardonne E., Kedem R., Stone M., Fermionic characters and arbitrary highest-weight integrable bs -modules, Comm. Math. Phys., 2006, 264(2), 427–464 http://dx.doi.org/10.1007/s00220-005-1486-3 Zbl1233.17017
- [2] Baranović I., Combinatorial bases of Feigin-Stoyanovsky’s type subspaces of level 2 standard modules for D 4(1), Comm. Algebra, 2011, 39(3), 1007–1051 http://dx.doi.org/10.1080/00927871003639329 Zbl1269.17011
- [3] Calinescu C., Principal subspaces of higher-level standard -modules, J. Pure Appl. Algebra, 2007, 210(2), 559–575 http://dx.doi.org/10.1016/j.jpaa.2006.10.018
- [4] Calinescu C., Intertwining vertex operators and certain representations of , Commun. Contemp. Math., 2008, 10(1), 47–79 http://dx.doi.org/10.1142/S0219199708002703
- [5] Calinescu C., Lepowsky J., Milas A., Vertex-algebraic structure of the principal subspaces of certain A 1(1)-modules I: Level one case, Internat. J. Math., 2008, 19(1), 71–92 http://dx.doi.org/10.1142/S0129167X08004571 Zbl1184.17012
- [6] Calinescu C., Lepowsky J., Milas A., Vertex-algebraic structure of the principal subspaces of certain A 1(1)-modules II: Higher-level case, J. Pure Appl. Algebra, 2008, 212(8), 1928–1950 http://dx.doi.org/10.1016/j.jpaa.2008.01.003 Zbl1184.17013
- [7] Calinescu C., Lepowsky J., Milas A., Vertex-algebraic structure of the principal subspaces of level one modules for the untwisted affine Lie algebras of types A, D, E, J. Algebra, 2010, 323(1), 167–192 http://dx.doi.org/10.1016/j.jalgebra.2009.09.029 Zbl1221.17032
- [8] Capparelli S., Lepowsky J., Milas A., The Rogers-Ramanujan recursion and intertwining operators, Commun. Contemp. Math., 2003, 5(6), 947–966 http://dx.doi.org/10.1142/S0219199703001191 Zbl1039.05005
- [9] Capparelli S., Lepowsky J., Milas A., The Rogers-Selberg recursions, the Gordon-Andrews identities and intertwining operators, Ramanujan J., 2006, 12(3), 379–397 http://dx.doi.org/10.1007/s11139-006-0150-7 Zbl1166.17009
- [10] Dong C., Lepowsky J., Generalized Vertex Algebras and Relative Vertex Operators, Progr. Math., 112, Birkhäuser, Boston, 1993 http://dx.doi.org/10.1007/978-1-4612-0353-7 Zbl0803.17009
- [11] Feigin B., Jimbo M., Loktev S., Miwa T., Mukhin E., Bosonic formulas for (k; l)-admissible partitions, Ramanujan J., 2003, 7(4), 485–517, 519–530 http://dx.doi.org/10.1023/B:RAMA.0000012430.68976.c0 Zbl1039.05008
- [12] Feigin B., Jimbo M., Miwa T., Mukhin E., Takeyama Y., Fermionic formulas for (k; 3)-admissible configurations, Publ. Res. Inst. Math. Sci., 2004, 40(1), 125–162 http://dx.doi.org/10.2977/prims/1145475968 Zbl1134.17311
- [13] Feigin B., Jimbo M., Miwa T., Mukhin E., Takeyama Y., Particle content of the (k; 3)-configurations, Publ. Res. Inst. Math. Sci., 2004, 40(1), 163–220 http://dx.doi.org/10.2977/prims/1145475969 Zbl1062.05010
- [14] Frenkel I.B., Kac V.G., Basic representations of affine Lie algebras and dual resonance models, Invent. Math., 1980, 62(1), 23–66 http://dx.doi.org/10.1007/BF01391662 Zbl0493.17010
- [15] Frenkel I., Lepowsky J., Meurman A., Vertex Operator Algebras and the Monster, Pure Appl. Math., 134, Academic Press, Boston, 1988 Zbl0674.17001
- [16] Georgiev G., Combinatorial constructions of modules for infinite-dimensional Lie algebras I. Principal subspace, J. Pure Appl. Algebra, 1996, 112(3), 247–286 http://dx.doi.org/10.1016/0022-4049(95)00143-3
- [17] Jerković M., Recurrence relations for characters of affine Lie algebra A ℓ(1), J. Pure Appl. Algebra, 2009, 213(6), 913–926 http://dx.doi.org/10.1016/j.jpaa.2008.10.001 Zbl1183.17012
- [18] Jerković M., Recurrences and characters of Feigin-Stoyanovsky’s type subspaces, In: Vertex Operator Algebras and Related Areas, Contemp. Math., 497, American Mathematical Society, Providence, 2009, 113–123
- [19] Jerković M., Character formulas for Feigin-Stoyanovsky’s type subspaces of standard sl(3, ℂ)∧-modules, preprint avaliable at http://arxiv.org/abs/1105.2927
- [20] Kac V.G., Infinite-Dimensional Lie Algebras, 3rd ed., Cambridge University Press, Cambridge, 1990 http://dx.doi.org/10.1017/CBO9780511626234 Zbl0716.17022
- [21] Lepowsky J., Wilson R.L., The structure of standard modules I. Universal algebras and the Rogers-Ramanujan identities, Invent. Math., 1984, 77(2), 199–290; The structure of standard modules II. The case A 1(1), principal gradation, Invent. Math., 1985, 79(5), 417–442 http://dx.doi.org/10.1007/BF01388447 Zbl0577.17009
- [22] Primc M., Vertex operator construction of standard modules for A n(1), Pacific J. Math., 1994, 162(1), 143–187 Zbl0787.17024
- [23] Primc M., (k; r)-admissible configurations and intertwining operators, In: Lie Algebras, Vertex Operator Algebras and their Applications, Contemp. Math., 442, American Mathematical Society, Providence, 2007, 425–434 Zbl1152.17012
- [24] Segal G., Unitary representations of some infinite-dimensional groups, Commun. Math. Phys., 1981, 80(3), 301–342 http://dx.doi.org/10.1007/BF01208274 Zbl0495.22017
- [25] Stoyanovsky A.V., Feigin B.L., Functional models of the representations of current algebras, and semi-infinite Schubert cells, Funktsional. Anal. i Prilozhen., 1994, 28(1), 68–90 (in Russian) http://dx.doi.org/10.1007/BF01079010
- [26] Trupčević G., Combinatorial bases of Feigin-Stoyanovsky’s type subspaces of higher-level standard -modules, J. Algebra, 2009, 322(10), 3744–3774 http://dx.doi.org/10.1016/j.jalgebra.2009.07.024 Zbl1216.17008
- [27] Trupčević G., Combinatorial bases of Feigin-Stoyanovsky’s type subspaces of level 1 standard modules for , Comm. Algebra, 2010, 38(10), 3913–3940 http://dx.doi.org/10.1080/00927870903366827 Zbl1221.17026
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