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DAHA of rank 1 is defined by the relation $$ (T - t^{1/2})(T + t^{-1/2})=0~, \quad TXT=X^{-1}~, \quad TY^{-1}T=Y~, \quad Y^{-1}X^{-1}YXT^2q^{1/2}=1 .$$ To understand its representations, it is useful …

It is shown by Berest-Etingof-Ginzburg that there exist finite-dimensional irreducible representations of rational Cherednik algebra $H_c(S_n)$ of $A_{n-1}$ type if and only if the deformation paramet …

The $S$-matrix is given by \begin{equation} \frac{S_{ij}}{S_{00}}=S_{R_i}(q^{\rho})S_{R_j}(q^{\rho+R_i}) \end{equation} where $S_{R}(x_1,\cdots,x_N)$ is the Schur polynomial with highest weight $R$, …

I would like to know if there is a proof for the identity used in the superconformal index of 4d ${\cal N}=2$ gauge theory. In the paper by Rastelli el al, it was discovered that Eq. (10) is equal to …

Given a vector $\vec k=(k_1,k_2,\cdots)$ with $k_i$ are non-negative integers, the Newton polynomial $p_{\vec k}(x)$ is defined as \begin{equation} p_{\vec k}(x)=\prod_{j=1}^n p_j^{k_j}(x)~, \end{equa …