arXiv subjects

Sungsoon Kim

Publications and source records attributed to Sungsoon Kim.

3 recordsLinked to original sources

arXiv2018

Gröbner-Shirshov bases for Temperley-Lieb algebras of the complex reflection group of type $G(d,1,n)$

We construct a Gröbner-Shirshov basis of the Temperley-Lieb algebra $\mathfrak{T}(d,n)$ of the complex reflection group $G(d,1,n)$, inducing the standard monomials expressed by the generators $\{E_i\}$ of $\mathfrak{T}(d,n)$. This result generalizes the one for the Coxeter group of type $B_n$ in \cite{KimSSLeeDI}. We also give a combinatorial interpretation of the standard monomials of $\mathfrak{T}(d,n)$, relating to the fully commutative elements of the complex reflection group $G(d,1,n)$. In this way, we obtain the dimension formula of $\mathfrak{T}(d,n)$.

math.RA↗

arXiv2018

Gröbner-Shirshov bases for Temperley-Lieb algebras of types $B$ and $D$

For Temperley-Lieb algebras of types $B$ and $D$, we construct their Gröbner-Shirshov bases and the corresponding standard monomials.

math.RA↗

arXiv2018

Fully commutative elements of the complex reflection groups

We extend the usual notion of fully commutative elements from the Coxeter groups to the complex reflection groups. Then we decompose the sets of fully commutative elements into natural subsets according to their combinatorial properties, and investigate the structure of these decompositions. As a consequence, we enumerate and describe the form of these elements in the complex reflection groups.

math.GR↗