Categorification of the Vector Representation of U(so( 8,C ) )
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摘要: 为了范畴化U (so (8, ) ) 向量表示的n次张量积, 定义了一般线性李代数gln的伯恩斯坦-盖尔芬德-盖尔芬德 (Bernstein-Gelfand-Gelfand, BGG) 范畴O的若干子范畴, 这些子范畴Grothendieck群的复化范畴化了D4型李代数包络代数向量表示n次张量积的底空间;定义了BGG范畴O上的一系列投射函子用于范畴化U (so (8, ) ) 在张量积上的作用;得到hi (1≤i≤4) 可由一对函子 (Hi+, Hi-) (1≤i≤4) 范畴化, ei、fi (1≤i≤3) 分别由εi、Fi (1≤i≤3) 范畴化, e4、f4分别由一对函子 (ε4+, ε4-) (F4+, F4-) 范畴化.Abstract: To categorify the n-tensor products of vector representation of U (so (8, ) ) , some subcategoriees of Bernstein-Gelfand-Gelfand (BGG) category O of the general linear Lie algebra glnwere defined. The complexifications of their Grothendieck groups were used for categorifing base spaces of ntensor products of vector representation. And some projective endfunctors of BGG category O, which were used for categorifing the action of U (so (8, ) ) on n-tensor products of vector representation, were defined. It was got that hi (1≤i≤4) can be categorified by a pair of functors (Hi+, Hi-) (1≤i≤4) , ei, fi (1≤i≤3) , can be categorified by εi, Fi (1≤i≤3) , e4, f4 can be categorified by a pair of functors (ε4+, ε4-) , (F4+, F4-) , respectively.
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Keywords:
- vector representation /
- categorification /
- BGG category /
- projective functors
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