Representation Theory of the Nonstandard Hecke Algebra
نویسنده
چکیده
The nonstandard Hecke algebra Ȟr was defined in [11] to study the Kronecker problem. We study a quotient Ȟr,2 of Ȟr , called the nonstandard Temperley-Lieb algebra, which is simpler than Ȟr. It is defined to be the subalgebra of Hr,2⊗Hr,2 generated by Pi := C ′ i ⊗C ′ i +Ci ⊗Ci, i ∈ [r− 1], where Hr,2 is the Temperley-Lieb algebra and C i and Ci are Kazhdan-Lusztig basis elements. We give a complete description of the irreducible representations of Ȟr,2. We also find that the restriction of an Ȟr,2irreducible to Ȟr−1,2 is multiplicity free, and as a consequence, any Ȟr,2-irreducible possesses a seminormal basis that is unique to a diagonal transformation.
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