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Symmetric chains, Gelfand-Tsetlin chains, and the Terwilliger algebra of the binary Hamming scheme

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Title Symmetric chains, Gelfand-Tsetlin chains, and the Terwilliger algebra of the binary Hamming scheme
 
Creator SRINIVASAN, MK
 
Subject SPERNER PROPERTY
UPPER-BOUNDS
Symmetric chain decomposition
Gelfand-Tsetlin bases
Symmetric group
Terwilliger algebra
Explicit block diagonalization
 
Description The de Bruijn-Tengbergen-Kruyswijk (BTK) construction is a simple algorithm that produces an explicit symmetric chain decomposition of a product of chains. We linearize the BTK algorithm and show that it produces an explicit symmetric Jordan basis (SJB). In the special case of a Boolean algebra, the resulting SJB is orthogonal with respect to the standard inner product and, moreover, we can write down an explicit formula for the ratio of the lengths of the successive vectors in these chains (i.e., the singular values). This yields a new constructive proof of the explicit block diagonalization of the Terwilliger algebra of the binary Hamming scheme. We also give a representation theoretic characterization of this basis that explains its orthogonality, namely, that it is the canonically defined (up to scalars) symmetric Gelfand-Tsetlin basis.
 
Publisher SPRINGER
 
Date 2012-06-26T05:25:54Z
2012-06-26T05:25:54Z
2011
 
Type Article
 
Identifier JOURNAL OF ALGEBRAIC COMBINATORICS,34(2)301-322
0925-9899
http://dx.doi.org/10.1007/s10801-010-0272-2
http://dspace.library.iitb.ac.in/jspui/handle/100/13964
 
Language English