{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,12]],"date-time":"2025-10-12T03:42:26Z","timestamp":1760240546073,"version":"build-2065373602"},"reference-count":18,"publisher":"MDPI AG","issue":"3","license":[{"start":{"date-parts":[[2019,7,19]],"date-time":"2019-07-19T00:00:00Z","timestamp":1563494400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100002608","name":"Daegu University","doi-asserted-by":"publisher","award":["Daegu University Research Grant 2016"],"award-info":[{"award-number":["Daegu University Research Grant 2016"]}],"id":[{"id":"10.13039\/501100002608","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Axioms"],"abstract":"<jats:p>We explicitly calculate the branching functions arising from the tensor product decompositions between level 2 and principal admissible representations over      sl ^  2    . In addition, investigating the characters of the minimal series representations of super-Virasoro algebras, we present the tensor product decompositions in terms of the minimal series representations of super-Virasoro algebras for the case of principal admissible weights.<\/jats:p>","DOI":"10.3390\/axioms8030082","type":"journal-article","created":{"date-parts":[[2019,7,19]],"date-time":"2019-07-19T03:14:41Z","timestamp":1563506081000},"page":"82","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":1,"title":["Branching Functions for Admissible Representations of Affine Lie Algebras and Super-Virasoro Algebras"],"prefix":"10.3390","volume":"8","author":[{"given":"Namhee","family":"Kwon","sequence":"first","affiliation":[{"name":"Department of Mathematics, Daegu University, Gyeongsan, Gyeongbuk 38453, Korea"}]}],"member":"1968","published-online":{"date-parts":[[2019,7,19]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"1575","DOI":"10.1103\/PhysRevLett.52.1575","article-title":"Conformal invariance, unitarity and critical exponents in two dimensions","volume":"52","author":"Friedan","year":"1984","journal-title":"Phys. Rev. Lett."},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"223","DOI":"10.1016\/0370-1573(82)90087-4","article-title":"Superstring theory","volume":"83","author":"Schwarz","year":"1982","journal-title":"Physics Rep."},{"key":"ref_3","unstructured":"Fulton, W., and Harris, J. (1991). Representation Theory: A First Course, Springer."},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"295","DOI":"10.1007\/BF02096589","article-title":"Characters and fusion rules for Walgebras via quantized Drinfeld-Sokolov reduction","volume":"147","author":"Frenkel","year":"1992","journal-title":"Comm. Math. Phys."},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"4956","DOI":"10.1073\/pnas.85.14.4956","article-title":"Modular invariant representations of infinite-dimensional Lie algebras and superalgebras","volume":"85","author":"Kac","year":"1988","journal-title":"Proc. Natl. Acad. Sci. USA"},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"156","DOI":"10.1016\/0001-8708(88)90055-2","article-title":"Modular and conformal invariance constraints in representation theory of affine algebras","volume":"70","author":"Kac","year":"1988","journal-title":"Adv. Math."},{"key":"ref_7","first-page":"138","article-title":"Classification of modular invariant representations of affine algebras","volume":"Volume 7","author":"Kac","year":"1989","journal-title":"Infinite-Dimensional Lie Algebras and Groups"},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"307","DOI":"10.1007\/s00220-003-0926-1","article-title":"Quantum reduction for affine superalgebras","volume":"241","author":"Kac","year":"2003","journal-title":"Comm. Math. Phys."},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"3","DOI":"10.1007\/BF00053290","article-title":"Branching functions for winding subalgebras and tensor products","volume":"21","author":"Kac","year":"1990","journal-title":"Acta. Appl. Math."},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"125","DOI":"10.1016\/0001-8708(84)90032-X","article-title":"Infinite-dimensional Lie algebras, theta functions and modular forms","volume":"53","author":"Kac","year":"1984","journal-title":"Adv. Math."},{"key":"ref_11","doi-asserted-by":"crossref","unstructured":"Kac, V.G. (1990). Infinite Dimensional Lie Algebras, Cambridge University Press. [3rd ed.].","DOI":"10.1017\/CBO9780511626234"},{"key":"ref_12","doi-asserted-by":"crossref","unstructured":"Wakimoto, M. (2001). Infinite-Dimensional Lie Algebras, In Translation of Mathematical Monographs; American Mathematical Society.","DOI":"10.1090\/mmono\/195"},{"key":"ref_13","doi-asserted-by":"crossref","unstructured":"Wakimoto, M. (2001). Lectures on Infinite-Dimensional Lie Algebras, World Scientific.","DOI":"10.1142\/9789812810700"},{"key":"ref_14","doi-asserted-by":"crossref","unstructured":"Kac, V.G. (1998). Vertex Algebras for Beginners, American Mathematical Society. [2nd ed.].","DOI":"10.1090\/ulect\/010"},{"key":"ref_15","doi-asserted-by":"crossref","unstructured":"Kac, V.G., and Raina, A.K. (1987). Bombay Lectures on Highest Weight Representations, World Scientific.","DOI":"10.1142\/0476"},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1016\/S0001-8708(02)00059-2","article-title":"Representation theory of Neveu-Schwarz and Ramond algebra I: Verma modules","volume":"178","author":"Iohara","year":"2003","journal-title":"Adv. Math."},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"105","DOI":"10.1007\/BF01464283","article-title":"Unitary representations of the Virasoro and super-Virasoro algebras","volume":"103","author":"Goddard","year":"1986","journal-title":"Commun. Math. Phys."},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"345","DOI":"10.1007\/3540171630_93","article-title":"Unitarizable Highest Weight Representations of the Virasoro, Neveu-Schwarz and Ramond Algebras","volume":"Volume 261","author":"Barut","year":"1986","journal-title":"Proceedings of the Symposium on Conformal Groups and Structures, Lecture Notes in Physics"}],"container-title":["Axioms"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2075-1680\/8\/3\/82\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T13:07:21Z","timestamp":1760188041000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2075-1680\/8\/3\/82"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2019,7,19]]},"references-count":18,"journal-issue":{"issue":"3","published-online":{"date-parts":[[2019,9]]}},"alternative-id":["axioms8030082"],"URL":"https:\/\/doi.org\/10.3390\/axioms8030082","relation":{},"ISSN":["2075-1680"],"issn-type":[{"type":"electronic","value":"2075-1680"}],"subject":[],"published":{"date-parts":[[2019,7,19]]}}}