Characters, supercharacters and Weber modular functions
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Antun Milas
Abstract
We study certain canonical automorphic forms associated to irreducible characters of N = 1 superconformal minimal models in both the Neveu-Schwarz and Ramond sector by using representation theoretic methods. By extending the techniques from [A. Milas, Virasoro algebra, Dedekind eta-function and Specialized Macdonald's identities, Transf. Groups 9 (2004), 273–288.] to the setting of N = 1 superconformal algebras we obtain a series of modular identities involving certain Wronskian determinants in both Neveu-Schwarz (untwisted) and Ramond (twisted) sector. Three Weber modular functions play a fundamental role here as well as the Dedekind η-function. In the most interesting case of 
minimal series, we obtain a derivation and generalizations of several classical modular q-series identities (e.g., Jacobi's Four Square Theorem, a Carlitz' identity, specialized Macdonald's identities for B series, etc.)
© Walter de Gruyter
Articles in the same Issue
- Tangent spaces and Gromov-Hausdorff limits of subanalytic spaces
- Pinching estimates and motion of hypersurfaces by curvature functions
- Characters, supercharacters and Weber modular functions
- Three-dimensional Ricci solitons which project to surfaces
- Some q-analogues of the Carter-Payne theorem
- Preperiodic points of polynomials over global fields
- Orbit-counting in non-hyperbolic dynamical systems
- On intervals with few prime numbers
-
Bifurcation currents in holomorphic dynamics on
Articles in the same Issue
- Tangent spaces and Gromov-Hausdorff limits of subanalytic spaces
- Pinching estimates and motion of hypersurfaces by curvature functions
- Characters, supercharacters and Weber modular functions
- Three-dimensional Ricci solitons which project to surfaces
- Some q-analogues of the Carter-Payne theorem
- Preperiodic points of polynomials over global fields
- Orbit-counting in non-hyperbolic dynamical systems
- On intervals with few prime numbers
-
Bifurcation currents in holomorphic dynamics on
