| Budget Amount *help |
¥3,380,000 (Direct Cost: ¥2,600,000、Indirect Cost: ¥780,000)
Fiscal Year 2016: ¥780,000 (Direct Cost: ¥600,000、Indirect Cost: ¥180,000)
Fiscal Year 2015: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
Fiscal Year 2014: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
Fiscal Year 2013: ¥780,000 (Direct Cost: ¥600,000、Indirect Cost: ¥180,000)
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| Outline of Final Research Achievements |
We have introduced new quantities called partition q-series for quiver mutation sequences and proved fundamental properties in a joint work with Akishi Kato. One motivation is to provide a solid mathematical foundation to extract essential information of the partition function of a 3-dimensional gauge theory proposed in a joint work with Masahito Yamazaki. In particular, for quivers which are of Dynkin type or square products thereof with special mutation sequences, we have proved that partition q-series are identified with fermionic character formulas of certain modules associated with affine Lie algebras. Moreover, for reddening sequences, we have proved that a graded version of partition q-series essentially coincides with the combinatorial Donaldson-Thomas invariant.
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