中文摘要：

为了范畴化U（so（8,C））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@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@上的一系列投射函子用于范畴化U（so（8,C））在张量积上的作用;得到hi（1≤i≤4）可由一对函子（gl＋,gl-）（1≤i≤4）范畴化,ei（f）i（1≤i≤3）分别由εi、（F）（1≤i≤3）范畴化,e4（f）4分别由一对函子（ε4＋,ε4-）（（F）4＋,（F）-）范畴化.

英文摘要：

To categorify the n-tensor products of vector representation of U （so （8, C ））, somesubcategoriees of Bernstein-Gelfand-Gelfand （BGG） category @ of the general linear Lie algebra gln weredefined. The complexifications of their Grothendieck groups were used for categorifing base spaces of n- tensor products of vector representation. And some projective endfunctors of BGG category @, which wereused for categorifing the action of U （ so （8, C） ） on n-tensor products of vector representation, were defined. It was got that hi （1≤i≤4） can be c ategorified by a pair of functors （gl＋,gl-）（1≤i≤4）,ei（f）i（1≤i≤3）, can be categorified by εi、（F）（1≤i≤3）, e4 ,f4 can be categorified by a pair of functors （ε4＋,ε4-）（（F）4＋,（F）-）, respectively.