| Budget Amount *help |
¥8,320,000 (Direct Cost: ¥6,400,000、Indirect Cost: ¥1,920,000)
Fiscal Year 2013: ¥2,860,000 (Direct Cost: ¥2,200,000、Indirect Cost: ¥660,000)
Fiscal Year 2012: ¥2,470,000 (Direct Cost: ¥1,900,000、Indirect Cost: ¥570,000)
Fiscal Year 2011: ¥2,990,000 (Direct Cost: ¥2,300,000、Indirect Cost: ¥690,000)
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| Research Abstract |
We studied representation theory of graded Hecke algebras which are called quiver Hecke algebras. The quiver Hecke algebras were introduced for the purpose of categorifying integrable modules over quantum groups. In the early stage of the research, we proved certain nonnegativity result which was a property necessary to hold when we speak of categorification of Fock spaces. After that stage, we focused on categorification of basic modules over quantum groups of affine type. We were only able to handle the affine type A for long time. In the current research, we have succeeded in handling other affine types than affine type A and we have proved Erdmann-Nakano type theorems for finite quiver Hecke algebras. In particular, it allowed us to analyze finite quiver Hecke algebras of tame representation type in detail. Related to this analysis, we have classified two point symmetric special biserial algebras.
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