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pro vyhledávání: '"Terwilliger, Paul"'
Autor:
Terwilliger, Paul
The $q$-Onsager algebra $O_q$ is defined by two generators and two relations, called the $q$-Dolan/Grady relations. In 2019, Baseilhac and Kolb introduced two automorphisms of $O_q$, now called the Lusztig automorphisms. Recently, we introduced a gen
Externí odkaz:
http://arxiv.org/abs/2409.19815
Autor:
Terwilliger, Paul
Let $\Gamma$ denote a $Q$-polynomial distance-regular graph with diameter $D\geq 1$. For a vertex $x$ of $\Gamma$ the corresponding subconstituent algebra $T=T(x)$ is generated by the adjacency matrix $A$ of $\Gamma$ and the dual adjacency matrix $A^
Externí odkaz:
http://arxiv.org/abs/2408.11282
Autor:
Terwilliger, Paul
In 2023 we obtained a $Q$-polynomial structure for the projective geometry $L_N(q)$. In the present paper, we display a more general $Q$-polynomial structure for $L_N(q)$. Our new $Q$-polynomial structure is defined using a free parameter $\varphi$ t
Externí odkaz:
http://arxiv.org/abs/2407.14964
Autor:
Terwilliger, Paul
The tridiagonal algebra is defined by two generators and two relations, called the tridiagonal relations. Special cases of the tridiagonal algebra include the $q$-Onsager algebra, the positive part of the $q$-deformed enveloping algebra $U_q({\wideha
Externí odkaz:
http://arxiv.org/abs/2407.00551
Autor:
Nomura, Kazumasa, Terwilliger, Paul
Let ${\mathcal X} = (X, \{R_i\}_{i=0}^d)$ denote a symmetric association scheme. Fix an ordering $\{E_i\}_{i=0}^d$ of the primitive idempotents of $\mathcal{X}$, and let $P$ (resp.\ $Q$) denote the corresponding first eigenmatrix (resp.\ second eigen
Externí odkaz:
http://arxiv.org/abs/2405.10491
Autor:
Nomura, Kazumasa, Terwilliger, Paul
Let $\Gamma$ denote a $Q$-polynomial distance-regular graph, with vertex set $X$ and diameter $D\geq 3$. The standard module $V$ has a basis $\lbrace {\hat x} \vert x \in X\rbrace$, where ${\hat x}$ denotes column $x$ of the identity matrix $I \in {\
Externí odkaz:
http://arxiv.org/abs/2404.09346
Autor:
Nomura, Kazumasa, Terwilliger, Paul
Let $\Gamma$ denote a distance-regular graph, with vertex set $X$ and diameter $D\geq 3$. We assume that $\Gamma$ is formally self-dual and $q$-Racah type. We also assume that for each $x \in X$ the subconstituent algebra $T=T(x)$ contains a certain
Externí odkaz:
http://arxiv.org/abs/2308.11061
Autor:
Terwilliger, Paul
The goal of this article is to display a $Q$-polynomial structure for the Attenuated Space poset $\mathcal A_q(N,M)$. The poset $\mathcal A_q(N,M)$ is briefly described as follows. Start with an $(N+M)$-dimensional vector space $H$ over a finite fiel
Externí odkaz:
http://arxiv.org/abs/2307.07833
Autor:
Terwilliger, Paul
In 1998, Georgia Benkart and Tom Roby introduced the down-up algebra $\mathcal A$. The algebra $\mathcal A$ is associative, noncommutative, and infinite-dimensional. It is defined by two generators $A,B$ and two relations called the down-up relations
Externí odkaz:
http://arxiv.org/abs/2306.04770
Autor:
Nomura, Kazumasa, Terwilliger, Paul
Let $\F$ denote a field, and let $V$ denote a vector space over $\F$ with finite positive dimension. A Leonard pair on $V$ is an ordered pair of diagonalizable $\F$-linear maps $A: V \to V$ and $A^* : V \to V$ that each act on an eigenbasis for the o
Externí odkaz:
http://arxiv.org/abs/2304.04965