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    Invariant tensors and the cyclic sieving phenomenon

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    We construct a large class of examples of the cyclic sieving phenomenon by expoiting the representation theory of semi-simple Lie algebras. Let MM be a finite dimensional representation of a semi-simple Lie algebra and let BB be the associated Kashiwara crystal. For r0r\ge 0, the triple (X,c,P)(X,c,P) which exhibits the cyclic sieving phenomenon is constructed as follows: the set XX is the set of isolated vertices in the crystal rB\otimes^rB; the map c ⁣:XXc\colon X\rightarrow X is a generalisation of promotion acting on standard tableaux of rectangular shape and the polynomial PP is the fake degree of the Frobenius character of a representation of Sr\mathfrak{S}_r related to the natural action of Sr\mathfrak{S}_r on the subspace of invariant tensors in rM\otimes^rM. Taking MM to be the defining representation of SL(n)\mathrm{SL}(n) gives the cyclic sieving phenomenon for rectangular tableaux

    Data Processing In The Texas A & M University Library

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    The Texas A & M University Library embraced automation as a way of life when it became the first library in the Southwest to employ a Data Processing Supervisor as a full-time Library staff member in September, 1964. The creation of such a position as part of the Library staff was only one of several favorable circumstances which combined to provide the necessary foundation for the achievements outlined in this paper. In addition to an enthusiastic University administration which provided requested supplemental funds for a special conversion project, the Library has access to the University's centralized data processing facility, which is one of the largest such University installations in the Southwest. The Data Processing Center houses an IBM 7094-1401 computer system with 14 magnetic tape drives, two separate off-line 1401 tape systems (one with a 1404 printer), and a battery of high speed sorters, collators, and card punches. This tremendous hardware capability has proved to be a great asset to our automation program.published or submitted for publicatio

    Eleven Years Under the Indiana Horizontal Property Act

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