2009 Fiscal Year Final Research Report
ANALYSIS ON INVARIANTS ASSOCIATED WITH PREHOMOGENEOUS VECTOR SPACES FROM THE VIEW POINT OF REPRESENTATION THEORY
| Project/Area Number |
19740003
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| Research Category |
Grant-in-Aid for Young Scientists (B)
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| Allocation Type | Single-year Grants |
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| Research Field |
Algebra
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| Research Institution | Chiba Institute of Technology (2008-2009)
University of Tsukuba (2007) |
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Principal Investigator |
SUGIYAMA Kazunari Chiba Institute of Technology, 情報科学部, 助教 (90375395)
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| Project Period (FY) |
2007 – 2009
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| Keywords | 概均質ベクトル空間 |
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| Research Abstract |
We have studied the b-functions of relative invariants of the prehomogeneous vector spaces associated with quivers of type A. By applying the decomposition formula for b-functions, we determine explicitly the b-functions of one-variable for each irreducible relative invariant. Moreover, we give a graphical algorithm to determine the b-functions of several variables. As its application, we have obtained some results on functional equations of prehomogeneous vector spaces of parabolic type arising from special linear Lie algebras.
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