To each partition λ, we introduce a measure Sλ(x; t)sλ(y)/Zt where sλ is the Schur function and Sλ(x; t) is a generalization of the Schur function defined in [M] and Zt is a normalization constant. This measure, which we call the t-Schur measure, is a generalization of the Schur measure [O] and the shifted Schur measure studied by Tracy and Widom [TW3]. We prove that by a certain specialization...

Young’s lattice, the lattice of all Young diagrams, has the Robinson-Schensted-Knuth correspondence, the correspondence between certain matrices and pairs of semi-standard Young tableaux with the same shape. Fomin introduced generalized Schur operators to generalize the Robinson-Schensted-Knuth correspondence. In this sense, generalized Schur operators are generalizations of semi-standard Young...

Schur Q-functions were originally introduced by Schur in relation to projective representations of the symmetric group and they can be defined combinatorially in terms of shifted tableaux. In this paper we describe planar decompositions of shifted tableaux into strips and use the shapes of these strips to generate pfaffi.ans and determinants that are equal to Schur Q-functions. As special cases...

We introduce a new basis for the algebra of quasisymmetric functions that naturally partitions Schur functions, called quasisymmetric Schur functions. We describe their expansion in terms of fundamental quasisymmetric functions and determine when a quasisymmetric Schur function is equal to a fundamental quasisymmetric function. We conclude by describing a Pieri rule for quasisymmetric Schur fun...

Multiplication is a basic operation in any signal processing application. Multiplication is the most important one among the four arithmetic operations like addition, subtraction, and division. Multipliers are usually hardware intensive, and the main parameters of concern are high speed, low cost, and less VLSI area. The propagation time and power consumption in the multiplier are always high. ...

We present a survey of recent developments of the Beilinson–Lusztig–MacPherson approach in the study of quantum gl n , infinitesimal quantum gl n , quantum gl ∞ and their associated q-Schur algebras, little q-Schur algebras and infinite q-Schur algebras. We also use the relationship between quantum gl ∞ and infinite q-Schur algebras to discuss their representations.

Using operators on compositions we develop further both the theory of quasisymmetric Schur functions and of noncommutative Schur functions. By establishing relations between these operators, we show that the posets of compositions arising from the right and left Pieri rules for noncommutative Schur functions can each be endowed with both the structure of dual graded graphs and dual filtered gra...

The Schur multiplier M(Ḡ1) ≅4 of the maximal subgroup Ḡ1 = 2⁶˙G₂(2)of Rudvalis sporadic simple group Ru is a cyclic order 4. Hence full representative R type 4.(2⁶˙G₂(2)) exists for Ḡ1. Furthermore, will have four sets IrrProj(Ḡ1;αi) irreducible projective characters, where associated factor α1, α2, α3 and α4, orders 1, 2, 4 4, respectively. In this paper, we deal with 2-fold cover 2. which can...

Abstract We establish several new characterizations of amenable $W^*$ - and $C^*$ -dynamical systems over arbitrary locally compact groups. In the -setting we show that amenability is equivalent to (1) a Reiter property (2) existence certain net completely positive Herz–Schur multipliers $(M,G,\alpha )$ converging point weak* identity $G\bar {\ltimes }M$ . -setting, prove $(A,G,\alpha an analog...

Many results involving Schur functions have analogues involving k-Schur functions. Standard strong marked tableaux play a role for k-Schur functions similar to the role standard Young tableaux play for Schur functions. We discuss results and conjectures toward an analogue of the hook-length formula.