scholarly journals Tridiagonal pairs and the q-tetrahedron algebra

2009 ◽  
Vol 431 (5-7) ◽  
pp. 903-925 ◽  
Author(s):  
Darren Funk-Neubauer
Keyword(s):  
Tridiagonal Pairs

scholarly journals Tridiagonal pairs of type III with height one

2019 ◽  
Vol 35 (1) ◽  
pp. 555-582 ◽  
Author(s):  
Xue Li ◽  
Bo Hou ◽  
Suogang Gao
Keyword(s):  
Type Iii ◽  
Tridiagonal Pairs

scholarly journals A classification of sharp tridiagonal pairs

2011 ◽  
Vol 435 (8) ◽  
pp. 1857-1884 ◽  
Author(s):  
Tatsuro Ito ◽  
Kazumasa Nomura ◽  
Paul Terwilliger
Keyword(s):  
Tridiagonal Pairs

scholarly journals Tridiagonal pairs and the μ-conjecture

2009 ◽  
Vol 430 (1) ◽  
pp. 455-482 ◽  
Author(s):  
Kazumasa Nomura ◽  
Paul Terwilliger
Keyword(s):  
Tridiagonal Pairs

scholarly journals Tridiagonal pairs of q-Racah type

2009 ◽  
Vol 322 (1) ◽  
pp. 68-93 ◽  
Author(s):  
Tatsuro Ito ◽  
Paul Terwilliger
Keyword(s):  
Tridiagonal Pairs

scholarly journals Tridiagonal pairs of Krawtchouk type

2007 ◽  
Vol 427 (2-3) ◽  
pp. 218-233 ◽  
Author(s):  
Tatsuro Ito ◽  
Paul Terwilliger
Keyword(s):  
Tridiagonal Pairs

scholarly journals Towards a classification of the tridiagonal pairs

2008 ◽  
Vol 429 (2-3) ◽  
pp. 503-518 ◽  
Author(s):  
Kazumasa Nomura ◽  
Paul Terwilliger
Keyword(s):  
Tridiagonal Pairs

scholarly journals Tridiagonal pairs of type III with height one

2019 ◽  
Vol 35 ◽  
pp. 555-582 ◽  
Author(s):  
Xue Li ◽  
Bo Hou ◽  
Suogang Gao
Keyword(s):  
Vector Space ◽  
Closed Field ◽  
Positive Dimension ◽  
Algebraically Closed Field ◽  
Type Iii ◽  
Tridiagonal Pairs ◽  
Unique Integer ◽  
Tridiagonal Pair

Let K denote an algebraically closed field with characteristic 0. Let V denote a vector space over K with finite positive dimension, and let A, A∗ denote a tridiagonal pair on V  of diameter d.  Let V0, . . . , Vd  denote a standard ordering of  the eigenspaces of A on V , and let θ0, . . . , θd denote the corresponding eigenvalues of A. It is assumed that d ≥ 3.  Let ρi  denote the dimension of Vi. The sequence ρ0, ρ1, . . . , ρd is called the shape of the tridiagonal pair. It is known that ρ0 = 1 and there  exists  a  unique  integer  h (0 ≤ h ≤ d/2)  such  that  ρi−1 < ρi  for  1 ≤ i ≤ h,  ρi−1 = ρi  for  h < i ≤ d − h,  and  ρi−1 > ρi for d − h < i ≤ d. The integer h is known as the height of the tridiagonal pair. In this paper, it is showed that the shape of a tridiagonal pair of type III with height one is either 1, 2, 2, . . ., 2, 1 or 1, 3, 3, 1.  In each case, an interesting basis is found for V and the actions of A, A∗ on this basis are described.

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