Far East Journal of Mathematical Sciences (FJMS)

The Far East Journal of Mathematical Sciences (FJMS) publishes original research papers and survey articles in pure and applied mathematics, statistics, mathematical physics, and other related fields. It welcomes application-oriented work as well.

Submit Article

A CATEGORICAL APPROACH TO RELAXED HIGHEST WEIGHT MODULES

Authors

  • Namhee Kwon

Keywords:

Lie superalgebras, affine Lie superalgebras, highest weight modules, relaxed highest weight modules, Verma modules, categories, enough projective objects

DOI:

https://doi.org/10.17654/0972087123009

Abstract

We introduce a category that is closed under the dual functor and contains relaxed highest weight modules. We also construct a category containing generalized Verma modules which yields a subcategory involving enough projective objects.

Received: April 2, 2023
Accepted: May 10, 2023

References

D. Adamovic and A. Milas, Vertex operator algebras associated to modular invariant representations of Math. Res. Lett. 2 (1995), 563-575.

T. Arakawa, Vanishing on cohomology associated to quantized Drinfeld-Sokolov reduction, Int. Math. Res. Notices 15 (2004), 729-767.

T. Arakawa, Representation theory of superconformal algebras and the Kac-Roan-Wakimoto conjecture, Duke Math. J. 130 (2005), 435-478.

T. Arakawa, Representation theory of W-algebras, Invent. Math. 169 (2007), 219-320.

B. Feigin, A. Semikhatov and I. Y. Tipunin, Equivalence between chain categories of representations of affine sl(2) and superconformal algebras, J. Math. Phys. 39 (1998), 3865-3905.

M. Gaberdiel, Fusion rules and logarithmic representations of a WZW model at fractional level, Nucl. Phys. B 618 (2001), 407-436.

J. E. Humphreys, Representations of semisimple Lie algebras in the BGG category , Graduate Studies in Mathematics 42, Amer. Math. Soc., Providence, RI, 2002.

V. G. Kac, Lie superalgebras, Adv. Math. 26 (1977), 8-96.

V. G. Kac and M. Wakimoto, Quantum reduction and representation theory of superconformal algebras, Adv. Math. 185 (2004), 400-458.

K. Kawasetsu and D. Ridout, Relaxed highest weight modules I: rank 1 cases, Comm. Math. Phys. 368 (2019), 627-663.

R. V. Moody and A. Pianzola, Lie algebras with triangular decompositions, Canad. Math. Soc. Ser. Monogr. Adv. Texts, Wiley, New York, 1995.

D. Ridout and S. Wood, Relaxed singular vectors, Jack symmetric functions and fractional level models, Nucl. Phys. B 894 (2015), 621-664.

W. Wang, Nilpotent orbits and finite W-algebras, Geometric Representation Theory and Extended Affine Lie Algebras, Fields Inst. Commun., Amer. Math. Soc., Providence, RI, Vol. 59, 2011, pp. 71-105.

Published

2023-05-16

Issue

Section

Articles

How to Cite

A CATEGORICAL APPROACH TO RELAXED HIGHEST WEIGHT MODULES. (2023). Far East Journal of Mathematical Sciences (FJMS), 140(2), 133-148. https://doi.org/10.17654/0972087123009

Similar Articles

You may also start an advanced similarity search for this article.