Some Representation Theory Of The Jl,n(δ) Algebra

In this thesis we study the representation theory of the algebra Jl,n(δ). We prove axioms (A5) and (A6) from the (CMPX) framework [3]. Then we have that the algebra Jl,n(δ) forms a tower of recollement. We give a set of generators for Jl,n(δ). We calculate the Gram determinants for the cell modules ∆0,n(n − 2,(2)) and ∆0,n(n − 2,(12 )). For the case l = 0 and when δ is not real, then the Gram determinants of these modules are not zero and hence J0,n(δ) is semisimple. While if the Gram determinants for ∆0,n(n − 2,(2)) and ∆0,n(n − 2,(12 )) are zero, we find some non-zero homomorphisms between some cell modules. We find that there are non-zero homomorphisms between ∆0,m(n,(2)) and ∆0,m(n − 2,(2)). Also we have non-zero homomorphisms between ∆0,m(n,(12 )) and ∆0,m(n − 2,(12 )).