Standard Lusztig bases and Schubert filtration for quantum Serre superalgebras of type~I (Q2719494)

This paper continues the author's investigation [ibid. 6, No. 1, 14-43 (1999; Zbl 0963.17009)]). The author constructs special bases called standard Lusztig bases in the quantum Serre superalgebras determined similarly to the known Lusztig bases in Drinfeld-Jimbo algebras [see \textit{D.~P.~Zhelobenko}, ``Representation of reductive Lie algebras'', Nauka, Moscow (1994; Zbl 0842.17007)]. Moreover, the relationship between these bases and the Schubert filtration determined by the kernels of some differential operators is studied. The main results [see \textit{D.~P.~Zhelobenko}, (loc. cit.) and Russ. Acad. Sci., Izv., Math. 43, No.~3, 397-419 (1994; Zbl 0822.17008); Vestn. Ross. Univ. Druzh. Nar., Ser. Mat. 2, No.~2, 3-13 (1995; Zbl 0963.17006)] are extended to the quantum Serre superalgebras of type~I.