KAZHDAN–LUSZTIG CELLS AND THE MURPHY BASIS

Kazhdan–lusztig Cells and the Murphy Basis

Let H be the Iwahori–Hecke algebra associated with Sn, the symmetric group on n symbols. This algebra has two important bases: the Kazhdan–Lusztig basis and the Murphy basis. While the former admits a deep geometric interpretation, the latter leads to a purely combinatorial construction of the representations of H, including the Dipper–James theory of Specht modules. In this paper, we establish...

The Murphy Clinics

we may orientate the position of any calculi and that the radiograph should be of both kidneys. Speaking of sarcomata which are inoperable he has had excellent results from the combined use of Coley's fluid, cacodylate of sodium, and X-rays. Sodium cacodylate is given hypodermically, 2, 3, or 4 grains being administered daily and then increasing the dose to 10 grains every third or fourth day. ...

Murphy McCaleb

This paper examines small ensemble interaction from the perspective of reflective practice. Current research on ensembles has increasingly focused on determining communicative properties of performers’ physical gestures. Interpretative coordination, although mentioned by Goodman (2002) and Williamon and Davidson (2002), has not been extensively explored. I argue that interpretative ensemble col...

Skein theory and the Murphy operators

The Murphy operators in the Hecke algebra Hn of type A are explicit commuting elements whose sum generates the centre. They can be represented by simple tangles in the Homfly skein theory version of Hn. In this paper I present a single tangle which represents their sum, and which is obviously central. As a consequence it is possible to identify a natural basis for the Homfly skein of the annulu...

Murphy Was an Optimist