• East Asian mathematical journal
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• v.25 no.4
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• pp.469-479
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• 2009

Temperley-Lieb algebras had been generalized to web spaces for rank 2 simple Lie algebras which led us to link invariants for these Lie algebras as a generalization of Jones polynomial. Recently, Geer found a new generalization of Jones polynomial for some Lie superalgebras. In this paper, we study the quantum sl(1|1) representation theory using the web space and find a finite presentation of the representation category (for generic q) of the quantum sl(1|1).

• Communications of the Korean Mathematical Society
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• v.23 no.3
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• pp.349-356
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• 2008

In this paper, we generalize the Catalan number to the (n, k)-th Catalan numbers and find a combinatorial description that the (n, k)-th Catalan numbers is equal to the number of partitions of n(k-1)+2 polygon by (k+1)-gon where all vertices of all (k+1)-gons lie on the vertices of n(k-1)+2 polygon.