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Rutgers University

1. Nandi, Debajyoti, 1980-. Partition identities arising from the standard A(2)2-modules of level 4.

Degree: PhD, Mathematics, 2014, Rutgers University

URL: https://rucore.libraries.rutgers.edu/rutgers-lib/45379/

In this dissertation, we propose a set of new partition identities, arising from a twisted vertex operator construction of the level 4 standard modules for the affine Kac-Moody algebra of type A(2)2 . These identities have an interesting new feature, absent from previously known examples of this type. This work is a continuation of a long line of research of constructing standard modules for affine Kac-Moody algebras via vertex operators, and the associated combinatorial identities. The interplay between representation theory and combinatorial identities was exemplified by the vertex-algebraic proof of the famous Rogers-Ramanujan-type identities using standard A(1)1-modules by J. Lepowsky and R. Wilson. In his Ph.D. thesis, S. Capparelli proposed new combinatorial identities using a twisted vertex operator construction of the standard A(2)2-modules of level 3, which were later proved independently by G. Andrews, S. Capparelli, and M. Tamba-C. Xie. We begin with an obvious spanning set for each of the level 4 standard modules for A(2)2 , and reduce this spanning set using various relations. Most of these relations come from certain product generating function identities which are valid for all the level 4 modules. There are also other ad-hoc relations specific to a particular module of level 4. In this way, we reduce our spanning sets to match with the graded dimensions of the said modules as closely as possible. We conjecture and present strong evidence for three partition identities based on the spanning sets for the three standard A(2)2-modules of level 4. One surprising result of our work is the discovery of relations of arbitrary length. Consequently, the partitions corresponding to these spanning sets cannot be described by difference conditions of finite length. The spanning set result proves one inequality of the proposed identities. There is strong evidence for the validity of the conjecture (i.e., the opposite inequality), since it has been verified to hold for partitions of n ≤ 170, and n = 180, 190 and 200.

Subjects/Keywords: Affine algebraic groups; Lie algebras

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APA (6^{th} Edition):

Nandi, Debajyoti, 1. (2014). Partition identities arising from the standard A(2)2-modules of level 4. (Doctoral Dissertation). Rutgers University. Retrieved from https://rucore.libraries.rutgers.edu/rutgers-lib/45379/

Chicago Manual of Style (16^{th} Edition):

Nandi, Debajyoti, 1980-. “Partition identities arising from the standard A(2)2-modules of level 4.” 2014. Doctoral Dissertation, Rutgers University. Accessed September 21, 2020. https://rucore.libraries.rutgers.edu/rutgers-lib/45379/.

MLA Handbook (7^{th} Edition):

Nandi, Debajyoti, 1980-. “Partition identities arising from the standard A(2)2-modules of level 4.” 2014. Web. 21 Sep 2020.

Vancouver:

Nandi, Debajyoti 1. Partition identities arising from the standard A(2)2-modules of level 4. [Internet] [Doctoral dissertation]. Rutgers University; 2014. [cited 2020 Sep 21]. Available from: https://rucore.libraries.rutgers.edu/rutgers-lib/45379/.

Council of Science Editors:

Nandi, Debajyoti 1. Partition identities arising from the standard A(2)2-modules of level 4. [Doctoral Dissertation]. Rutgers University; 2014. Available from: https://rucore.libraries.rutgers.edu/rutgers-lib/45379/

2. Durst, Susan, 1985-. Universal labeling algebras as invariants of layered graphs.

Degree: Mathematics, 2013, Rutgers University

URL: http://hdl.rutgers.edu/1782.1/rucore10001600001.ETD.000068846

Subjects/Keywords: Mathematics – Charts, diagrams, etc.; Algebra, Universal

Record Details Similar Records

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APA · Chicago · MLA · Vancouver · CSE | Export to Zotero / EndNote / Reference Manager

APA (6^{th} Edition):

Durst, Susan, 1. (2013). Universal labeling algebras as invariants of layered graphs. (Thesis). Rutgers University. Retrieved from http://hdl.rutgers.edu/1782.1/rucore10001600001.ETD.000068846

Note: this citation may be lacking information needed for this citation format:

Not specified: Masters Thesis or Doctoral Dissertation

Chicago Manual of Style (16^{th} Edition):

Durst, Susan, 1985-. “Universal labeling algebras as invariants of layered graphs.” 2013. Thesis, Rutgers University. Accessed September 21, 2020. http://hdl.rutgers.edu/1782.1/rucore10001600001.ETD.000068846.

Note: this citation may be lacking information needed for this citation format:

Not specified: Masters Thesis or Doctoral Dissertation

MLA Handbook (7^{th} Edition):

Durst, Susan, 1985-. “Universal labeling algebras as invariants of layered graphs.” 2013. Web. 21 Sep 2020.

Vancouver:

Durst, Susan 1. Universal labeling algebras as invariants of layered graphs. [Internet] [Thesis]. Rutgers University; 2013. [cited 2020 Sep 21]. Available from: http://hdl.rutgers.edu/1782.1/rucore10001600001.ETD.000068846.

Note: this citation may be lacking information needed for this citation format:

Not specified: Masters Thesis or Doctoral Dissertation

Council of Science Editors:

Durst, Susan 1. Universal labeling algebras as invariants of layered graphs. [Thesis]. Rutgers University; 2013. Available from: http://hdl.rutgers.edu/1782.1/rucore10001600001.ETD.000068846

Not specified: Masters Thesis or Doctoral Dissertation