Types

Abstract

This chapter divides the prototypes into much smaller units called types. It fixes a top and bottom row, and therefore a cartoon. For each episode ε‎ of the cartoon, the chapter fixes an integer κ‎subscript Greek small letter epsilon. Then the set of all short Gelfand-Tsetlin patterns with the given top and bottom rows is called a type. Thus two patterns are in the same type if and only if they have the same top and bottom rows (and hence the same cartoon), and if the sum of the first (middle) row elements in each episode is the same for both patterns. The possible episodes may be grouped into four classes: Class I, II, III, and IV.