scholarly journals Quantum groups and functional relations for higher rank

2014 ◽  
Vol 47 (27) ◽  
pp. 275201 ◽  
Author(s):  
Hermann Boos ◽  
Frank Göhmann ◽  
Andreas Klümper ◽  
Khazret S Nirov ◽  
Alexander V Razumov
Author(s):  
Thomas Creutzig ◽  
Matthew Rupert

We construct families of commutative (super) algebra objects in the category of weight modules for the unrolled restricted quantum group [Formula: see text] of a simple Lie algebra [Formula: see text] at roots of unity, and study their categories of local modules. We determine their simple modules and derive conditions for these categories being finite, non-degenerate, and ribbon. Motivated by numerous examples in the [Formula: see text] case, we expect some of these categories to compare nicely to categories of modules for vertex operator algebras. We focus in particular on examples expected to correspond to the higher rank triplet vertex algebra [Formula: see text] of Feigin and Tipunin and the [Formula: see text] algebras.


2014 ◽  
Vol 26 (06) ◽  
pp. 1430005 ◽  
Author(s):  
Herman Boos ◽  
Frank Göhmann ◽  
Andreas Klümper ◽  
Khazret S. Nirov ◽  
Alexander V. Razumov

We collect and systematize general definitions and facts on the application of quantum groups to the construction of functional relations in the theory of integrable systems. As an example, we reconsider the case of the quantum group [Formula: see text] related to the six-vertex model. We prove the full set of the functional relations in the form independent of the representation of the quantum group in the quantum space and specialize them to the case of the six-vertex model.


2003 ◽  
Vol 19 (3) ◽  
pp. 164-174 ◽  
Author(s):  
Stephen N. Haynes ◽  
Andrew E. Williams

Summary: We review the rationale for behavioral clinical case formulations and emphasize the role of the functional analysis in the design of individualized treatments. Standardized treatments may not be optimally effective for clients who have multiple behavior problems. These problems can affect each other in complex ways and each behavior problem can be influenced by multiple, interacting causal variables. The mechanisms of action of standardized treatments may not always address the most important causal variables for a client's behavior problems. The functional analysis integrates judgments about the client's behavior problems, important causal variables, and functional relations among variables. The functional analysis aids treatment decisions by helping the clinician estimate the relative magnitude of effect of each causal variable on the client's behavior problems, so that the most effective treatments can be selected. The parameters of, and issues associated with, a functional analysis and Functional Analytic Clinical Case Models (FACCM) are illustrated with a clinical case. The task of selecting the best treatment for a client is complicated because treatments differ in their level of specificity and have unequally weighted mechanisms of action. Further, a treatment's mechanism of action is often unknown.


Reflection ◽  
2018 ◽  
Vol 6 (1) ◽  
pp. 188-193
Author(s):  
Y. V. Falina ◽  
◽  
V. A. Obodov ◽  
V. V. Pankin ◽  
A. A. Smirnov ◽  
...  

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