Symmetric quivers, invariant theory, and saturation theorems for the classical groups

Details Symmetric quivers, invariant theory, and saturation theorems for the classical groups Symmetric quivers, invariant theory, and saturation theorems for the classical groups

2010-09-15

arxiv.org/abs/1009.3040v2

Adv. Math. 229 (2012), no. 2, 1104-1135

Mathematics

Representation Theory

29 pages, no figures; v2: updated Theorem 2.4 to odd characteristic, added Remark 3.9, added references, corrected some defini

Scientific paper

10.1016/j.aim.2011.10.009

Let G denote either a special orthogonal group or a symplectic group defined over the complex numbers. We prove the following saturation result for G: given dominant weights \lambda^1, ..., \lambda^r such that the tensor product V_{N\lambda^1} \otimes ... \otimes V_{N\lambda^r} contains nonzero G-invariants for some N \ge 1, we show that the tensor product V_{2\lambda^1} \otimes ... \otimes V_{2\lambda^r} also contains nonzero G-invariants. This extends results of Kapovich-Millson and Belkale-Kumar and complements similar results for the general linear group due to Knutson-Tao and Derksen-Weyman. Our techniques involve the invariant theory of quivers equipped with an involution and the generic representation theory of certain quivers with relations.

Affiliated with

Also associated with

No associations

Rating

Symmetric quivers, invariant theory, and saturation theorems for the classical groups does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Symmetric quivers, invariant theory, and saturation theorems for the classical groups, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Symmetric quivers, invariant theory, and saturation theorems for the classical groups will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-26875