Proves classical freeness of level-1 sl_n hat simple VOAs by using Dousse-Konan colored partition identities to build Gröbner bases for the associated arc algebras.
Characters of level 1 st andard modules of C (1) n as generating functions for generalised partitions
6 Pith papers cite this work. Polarity classification is still indexing.
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UNVERDICTED 6representative citing papers
The authors relate the remaining two Capparelli-Meurman-Primc-Primc conjectures to non-standard specializations of standard modules for A_{2n}^{(2)} and D_{n+1}^{(2)} using prior Rogers-Ramanujan work for affine Lie algebras.
Proves a new grounded partition identity of type D_4^(3) by equating Lepowsky's product formula to a sum obtained from perfect crystals via the Dousse-Konan technique.
The paper finds bivariate generating functions and bijections for the k=1 cases of conjectured colored partition identities, linking them to Andrews-Gordon identities and known results of Jing et al.
The paper combinatorially constructs and extends known positive series for k=1 CMPP partitions via base partitions and moves, supplying missing cases from prior symbolic work.
Two examples are given where combinatorial counting of relations among relations for C_n^(1) standard modules at level 5 and C_3^(1) at higher levels matches the representation-theoretic dimension in a trapezoid of negative root vectors.
citing papers explorer
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Classical freeness of $\widehat{\mathfrak{sl}}_n$ at level $1$ via combinatorics
Proves classical freeness of level-1 sl_n hat simple VOAs by using Dousse-Konan colored partition identities to build Gröbner bases for the associated arc algebras.
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Remarks on the conjectures of Capparelli, Meurman, Primc and Primc
The authors relate the remaining two Capparelli-Meurman-Primc-Primc conjectures to non-standard specializations of standard modules for A_{2n}^{(2)} and D_{n+1}^{(2)} using prior Rogers-Ramanujan work for affine Lie algebras.
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A New Grounded Partition Identity of Type $D_4^{(3)}$
Proves a new grounded partition identity of type D_4^(3) by equating Lepowsky's product formula to a sum obtained from perfect crystals via the Dousse-Konan technique.
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Companions to the Andrews-Gordon and Andrews-Bressoud Identities and Recent Conjectures of Capparelli, Meurman, Primc, and Primc
The paper finds bivariate generating functions and bijections for the k=1 cases of conjectured colored partition identities, linking them to Andrews-Gordon identities and known results of Jing et al.
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Combinatorial construction of known positive series for partition classes defined by Capparelli, Meurman, Primc, and Primc in the $k$=1 Case
The paper combinatorially constructs and extends known positive series for k=1 CMPP partitions via base partitions and moves, supplying missing cases from prior symbolic work.
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Two examples of combinatorial relations among relations of $C_{n}\sp{(1)}$-standard modules for higher levels
Two examples are given where combinatorial counting of relations among relations for C_n^(1) standard modules at level 5 and C_3^(1) at higher levels matches the representation-theoretic dimension in a trapezoid of negative root vectors.